Cosas del mundo real (actuarial)

Model Points for Asset Liability Models

A model point is an aggregate of policies, that should be a good representation
of a cluster of policies. However what does “good” mean? If we think of what
present value the original policies produce, and compare the resulting present
value when using our model points, then we do have an indication of the quality
of our model points. An additional criterion, is that we do not want too many
of those, otherwise we do not see any computation time reduction.
A typical liability model can be grouped in three components: scenarios,
policies and attributes. As already stated, scenarios are calculated by a scenario
generator and we have assumed that they are already optimized. Therefore they
are assumed to be really dierent and necessary, which means that there is no
further grouping to be done here. The attributes are characteristics of the policy
holder (age, sex, insured amount, etc) and product specics (duration, product,
premium, etc.). These are necessary to dene the product. Furthermore the
amount of attributes a policy has could be around 50, as compared to the
number of policies, of which there are innitely many. This means it is the
policies that we can group together. This is done, in such a way that, if policies
do resemble one another, we can simply group them in a new ctional policy,
which represents the individual policies. This is called the model point.

Arenga actuarial

Por sus pintas a ese profe le quedaría bien un bajo en sus manos y tocar versiones de metallica, o andar a caballo limpiando las costas de invasores. Pero no, la realidad es otra.

Nos ha saludado, se ha sentado en la mesa de la primera fila, y con una voz calmada y profunda nos ha dicho que los planes públicos es una asignatura dinámica, sujeta a cambios que no sólo vienen en camino sino que hasta pueden anticiparse. Que todo el mundo habla de las pensiones públicas porque todo el mundo está involucrado en ellas, y que hay noticias siempre, por todas partes, y que todo el mundo opina. ¿Y quiénes son los actuarios? Los actuarios son quienes miden el equilibrio entre el dinero que se tiene hoy y el valor actual actuarial de las prestaciones futuras.

¿El dinero que se tiene hoy, es suficiente?

Cuando Rajoy decidió subir un punto porcentual las pensiones, ¿de cuánto dinero estamos hablando?

En España existen 8 millones de jubilados que cobran unos 100 mil millones de euros anuales. Y subiendo. ¿Cuánto van a subir? ¿se van a poder pagar?

En España hay 3 colegios de actuarios; 500 colegiados en Barcelona, 1500 en Madrid y unos 50 en el pais vasco. ¿Y qué dicen ellos sobre la subida de las pensiones? Los actuarios son los profesionales mejor cualificados para valorar cómo está el sistema público de previsión. Los actuarios son, por definición, quienes deberían aprobar o no las cuentas. El actuario no decidirá cuánto hay que pagar, o cómo se debería financiar el sistema, el actuario valora simplemente si lo que hoy hay en la caja es suficiente, o no. Si dentro de 25 años a este trabajador le quieres pagar una pensión de tanto, hoy tienes que apoquinar esto otro. Los actuarios no se equivocan, sólo cambian de criterio. Y si pides una valoración a 30 actuarios, tendrás 30 valoraciones diferentes.

8 millones de jubilados son 8 millones de votos. De votos efectivos, porque los abuelos son quienes van siempre a votar. Y ellos no votarán a nadie que les diga que les va a pagar menos.

Cuando dices “soy actuario” la gente entiende “anticuario”, o “acuario”, o cualquier tontería. Sin embargo el peso, la significancia, del trabajo del actuario es fundamental. La gente debe conocernos, y reconocer qué hace un actuario.

En 1995 el sistema entró en quiebra técnica. ¿Por qué sobrevivió? Porque entonces se incorporaron al mercado laboral las mujeres y los inmigrantes, y con ellos se inflaron los ingresos de la seguridad social. Hasta hoy.

Hace 9 años perdí una apuesta; aposté que el sistema de pensiones cambiaría de forma que para calcular la pensión se tendría en cuenta toda la vida laboral, tanto ingresas tanto percibes. Entonces nadie cambió nada. Hubo un atentado, el PP salió del poder, entró el PSOE, y nadie quería llevarse mal con los jubilados y hacerles cobrar menos. Hoy esa apuesta la habría ganado, y no porque nadie de aquí lo haya decidido. Ha sido Europa la que ha dicho que esto tiene que cambiar.

Yo no soy profesor, soy actuario, y hacer estas clases es una penitencia.

Yo digo, bendita penitencia.

Examen de estadística actuarial aplicada

Pues he hecho examenes largos, pero nunca ninguno con tantas hojas. Falta encuadernarlo.

Por suerte haber hecho la evaluación continuada libera un montón. Libera tanto, tanto, tanto -al menos a mí- que casi ni me había estudiado el examen. Algunas de las preguntas del test me han sonado a chino, las del Brownie, pero otras ya me las conocía después de todas las horas que le he dedicado a las prácticas.

El test eran 40 preguntas con un poquito de todo, desde cosas sencillas a otras un poco más concretas, y esas que me sonaban a chino.

La parte práctica era elegir uno de cuatro problemas, y yo me he quedado con el cluster, porque lo he visto mucho más descriptivo que analítico y por ahí me he lanzado.

Respecto a las pobres almas que han hecho evaluación única,… que el Salvador los acoja en su misericordia.

Examen AMED

Aplicaciones Microinformáticas para la Estadística Descriptiva es una optativa sencilla de aprobar. Se le da un buen repaso a alguna operativa esencial de EXCEL (macros y sintaxis del VBA incluido) y se introduce al manejo de los datos de SPSS y de SAS (muy poquito este último).

Sacar nota ya es otro cuento.

Porque hoy no recordaba de memoria la sintaxis del SAS, y ya con eso he perdido algo más de un punto. Pedía manejar una base de datos y encontrar algunas medias y demás estadísticos de las variables.

Luego pedía manejar datos de una base de datos en EXCEL, algo que la versión del 2010 permite hacer de forma muy intuitiva, casi demasiado, y no sé si le habrá gustado que haya tomado el camino directo y fácil para hacer las cosas, aunque el resultado final esté bien.

Y sobre el SPSS me he líado un poquito, pero he descubierto una forma sencilla de “contar casos que cumplen una condición X y otra Y” y he resuelto la mitad del ejercicio copiando y pegando la misma orden.

El otro día lo hablaba con alguien, si esta asignatura vale 6 créditos me parece muy bien, pero proporcionalmente estadística aplicada, o planes privados, debería valer 24, porque realmente me he esforzado 4 veces más para estar al mismo nivel. Valen lo mismo y se parecen lo que un buitre a un calamar.

 

Tinyupload

Hace años que no me compro un periodico de papel, excepto en los aeropuertos al ir a volar, porque me parece una tontería comprar algo que explica lo sucedido ayer, cuando…

¿hace falta explicar lo que ofrecen los periódicos digitales?

Llevado a un cierto extremo, y ahora que estoy estudiando “planes privados de pensiones” como un idiota para el lunes que viene, me parece una tontería estudiar de pé a pá los requisitos, prestaciones, detalles y demás, de todo el tinglado de las ayudas económicas que existe en nuestro estado del bienestar. Es una tontería porque está todo actualizado y detallado en la web de la seguridad social. Bueno, tal vez no todo en un sentido absoluto, que claro que hay que aprender el motivo de las cosas, y los planes privados en sí, y hacer ejercicios,… pero es que tampoco hemos profundizado mucho en clase.

Es un despilfarro neuronal aprenderte de memoria lo que decía el periódico de ayer. Con el profe recitando en plan dictado de EGB.

En otros paises, por lo que me cuentan, normalmente los exámenes son más dinámicos, con el libro al lado, y con exposiciones orales, depende, y en general se valora más lo que dominas y entiendes que no tanto lo que recuerdas. No siempre, claro, pero sí normalmente.

Una de las grandezas del cerebro es la capacidad para apilar la información en bloques, y extraer lo que necesitas como quien estira un hilo, del que si tienes el mecanismo adecuado, puedes tirar y tirar y sacar toda la concatenación de ideas y conceptos que llevas dentro. No hace falta jugárselo todo a memorizar una cadena del proceso, es sólo cuestión de entenderlo bien. Es más real. Es lo que he vivido siempre en el trabajo: estar rodeado de herramientas y conocer qué hacer con ellas. Y la memoria pues sí, pero por rutinas, no por necesidad.

Una vez en un examen de contabilidad me quedé en blanco. Me lo había estudiado todo pero no encontraba el hilo a partir del cuál ir tirando. Al final hice lo que pude, con la conciencia distanciada de los recuerdos, y expuse las ideas generales que yo traia conmigo, pero no el proceso concreto que nos pedían en el ejercicio. Un mal día. A veces pasa. Pero siempre he pensado que esto es sólo una forma de puntuar tus conocimientos.

Actuarios europeos

Pues me respondieron unas dudas desde el col.legi d’actuaris de Barcelona, y me remitían a algo que desconocía: el grupo consultativo actuarial europeo: www.gcactuaries.org

Es un organismo que articula los diferentes colegios actuariales europeos, y busca una integración y colaboración entre estos profesionales. Por ejemplo, un documento detalla los conocimientos que se espera de un actuario (http://www.gcactuaries.org/documents/core_2005.pdf), y ayer ya publiqué otro que recoge la situación de emigrantes a otros paises. Siempre dentro de la zona euro, o al menos de los que han suscrito el acuerdo de reconocimiento.

Como decía Rubianes: Dios los cría y el viento los amontona.

Actuarios por el mundo

GROUPE CONSULTATIF ACTUARIEL EUROPEEN
EUROPEAN ACTUARIAL CONSULTATIVE GROUP

SECRETARIAT, MAISON DES ACTUAIRES, 4 PLACE DU SAMEDI
B-1000 BRUSSELS, BELGIUM
TELEPHONE: (+32) 28 30 01 99
E-MAIL: groupe@gcactuaries.org
WEB: www.gcactuaries.org

Date: November 2010
From:  Chairman, Groupe Consultatif
To:  Presidents of Member Associations of the Groupe Consultatif that are
signatories to the Agreement on the Mutual Recognition of
Qualifications
Copies to:  Presidents of Members Associations of the Groupe Consultatif that are
not signatories to the Agreement on the Mutual Recognition of
Qualifications
Members of the Groupe Consultatif
Members of the Standards, Freedoms and Professionalism Committee
Subject:  Guidelines for Application of the Agreement concerning the Mutual
Recognition by each Member Association of Members of the other
Associations

This Agreement was originally entered into in April 1991 by the member associations then
represented on the Groupe Consultatif and is based on the EU Directive 89/48/EEC (as
amended by Directive 2001/19/EC) for a general system for the recognition of higher
education diplomas awarded on completion of professional education and training of at least
three years’ duration.

The Agreement was updated in 1997 to include all member associations in the EU Member
States as well as the associations in Norway and Iceland by virtue of the European
Economic Area Agreement of May 1992, and again in 2004.  A separate, but parallel,
Agreement was entered into in 1997 by all associations subscribing to that Agreement and
the Association Suisse des Actuaires.  The recommendations made below applied equally
to that Agreement.  The Agreement was further revised in 2004 to reflect comments from
the European Commission’s Regulated Professions Unit, the further expansion of the
European Union, and the inclusion of the Association Suisse des Actuaires (replacing the
arrangement for a separate Agreement described above).  The latest update (November
2010) takes account of Directive 2005/36/EC on the recognition of professional
qualifications, and addresses concerns raised by members associations in relation to
disclosure of disciplinary proceedings.
In a letter of 31 May 1994 from the Chairman, Klaus Heubeck, the Groupe made a number
of recommendations to the Associations on how the Agreement should be interpreted and
implemented.  These recommendations were not mandatory but, in some cases, were
strongly recommended, whilst in other cases they were merely suggestions.  A revised
version of this original letter, containing a number of amendments, was issued in 2000 by
the then Chairman, Peter Clark, and further revisions were made in 2005 under the
chairmanship of Paul Grace – although the document has continued to be referred to as
“the Heubeck letter”.
The Groupe has reviewed the 2005 recommendations and, whilst the associations
subscribing to the Agreement are broadly content with them, a few further amendments
have been made.
1.  What is intended by a “fully-qualified actuary”?
A “fully–qualified actuary” is a member of an Association who is fully qualified to practice
as an actuary in the country of the Association.  As a minimum, all actuaries who are
recognised as fully-qualified must have completed an education programme which
complies with the requirements of the Groupe’s Core Syllabus; some associations may
also impose additional education or experience requirements.
Some Associations have only one grade of membership, and members of this grade
should all be “fully-qualified”.  Others have several grades; at least one of these should
comprise members who are fully qualified, but other grades might not – for example,
there might be a grade of “Honorary Fellow/Member”.  Where an association imposes
further requirements on its fully-qualified actuaries to obtain and maintain practising
certificates in specific areas of work, e.g. to become an Appointed Actuary, Pensions
Scheme Actuary, Actuarial Function Holder, or to hold other responsibilities which are
defined by statute, these requirements should apply equally to those actuaries admitted
under the Agreement.  The host association will be expected to issue a practising
certificate to a visiting actuary on the same basis as it applies to its own fully-qaulified
actuaries.
2.  Why should a migrant actuary be “encouraged” to apply for membership of the
host Association?
The Mutual Recognition Agreement cannot impose a requirement on an association that
its members working in another country join the host association, particularly since it
may not be compulsory for nationals of this country to be members of their home
association.  However, we consider that the home Association should strongly
encourage a migrant actuary to seek membership of the host Association for several
obvious reasons: for continuing professional development: it demonstrates a
professional attitude; to ensure awareness of, and compliance with, necessary codes of
practice and guidance notes; it may be required in order to carry out certain statutory
actuarial functions.  We also recommend that a migrant actuary be asked to report
annually to his or her home Association.
3.  How can a home Association help its members who take up work in another
country?
We recommend that Associations, through their Statutes and Codes of Practice, should
require their members to inform the (home) Association when they will be working for at
least 10% of their time (“pursue actively” in Paragraph 2 of the Mutual Recognition
Agreement) on actuarial business connected with another country.  This will enable the
home Association to advise the migrant actuary, when appropriate, of the rights and
obligations conferred by the Mutual Recognition Agreement.  The home Association will
be able to put the migrant actuary in touch with the appropriate host Association and
should, whenever possible, notify the host Association that one of its members will be
working in the host country.
4.  Should a migrant actuary’s duties be subject to the codes of practice of the home
Association or the host Association?
This is likely to be a significant issue where a migrant actuary is employed by a
multinational company, or undertakes work for a multinational client.  We consider it to
be essential that the terms of the actuary’s engagement drawn up before any work
starts should clearly specify which jurisdiction and national code(s) of practice the
migrant actuary will work to.
5.  Is it possible for an actuary to be granted full membership of the host Association
without being a full member of the home Association?
There may be times when a visiting actuary is not a member of his or her home
association.  In particular, there are circumstances where it is possible for a visiting
actuary to be accepted as fully-qualified in a host country on the basis of studies in his
or her home country even though these studies would not have been sufficient for full
qualification in his or her home country.  In such circumstances, it is considered
particularly important that a host Association should advise the home Association before
granting full membership on this basis.

6.  Should actuaries accepted into a host Association in terms of the Agreement, or
in terms of the Directives, be entitled to use the designatory letters or title of
members of the host Association?
As we understand the Directives a professionally qualified person recognised in a host
country in terms of the Directives can undertake all activities, whether regulated or not,
that can be undertaken by a full member of the association which they have joined and
is entitled to use the designatory letters or title of the host profession.  It is therefore
appropriate that a fully-qualified actuary practising in a host country should be able to
use the appropriate designatory letters or title of that Association.
However, we recommend the following practice: A distinction should be made between
titles obtained by study or examination (referred to as “home” qualifications), and titles
obtained only through implementation of the Agreement (“derived” qualifications).
Where qualifications are identified to clients or potential clients on stationery, visiting
cards, etc., the custom should be that an actuary may use all or any of his or her home
qualifications, but the derived qualification should be used only in the relevant country in
which he or she is providing services.  The actuary should not use more than one
derived qualification, and should not use the derived qualification except in
circumstances where it is essential to do so in order to show that he or she is qualified
in the host country to provide the relevant services.  A derived qualification should not
be used in the actuary’s home country.
It would therefore be necessary for an actuary who has obtained derived qualifications
in more than one host country to have different visiting cards, etc. in different countries.

7.  Should a host Association be able to cancel membership if a migrant actuary
ceases to provide services in the host country?
We consider that Associations should be entitled to grant “derived” memberships for life
if they wish to do so, but they should also have the right to cancel a host membership if
the actuary ceases to practise his or her profession in the host country.  Appropriate
practice might depend on the circumstances: an actuary who has worked for many
years in a host country and then retires to his or her home country, or to a third country,
might well expect to retain his or her derived membership; but an actuary who spends
only a short period in a host country might be expected to relinquish his or her
membership if he or she ceases to have any connection with that country.

8.  Should it be a condition that the migrant actuary retains membership of his or her
home Association?
We consider that an Association should be free, if it so wishes, to make derived
membership conditional on retention of the home qualification from which it is derived,
but it need not do so if it chooses not to.  We consider that good practice again would
depend on the circumstances.  A migrant actuary who has adopted a host country as
his or her own, and makes it his or her permanent residence and place of work, may
consider it appropriate to give up his or her original qualification if he or she has no
longer any contact with his or her home country or home Association.  But an actuary
who has acquired derived membership in a host country should not immediately
relinquish home qualifications and rely wholly on recently derived qualifications.  See
also the next question.  Where a migrant actuary has the option whether to maintain
membership of his or her home association, we recommend that he or she should do
so.

9.  Can a derived membership in one country be used to obtain derived membership
in another country?
We strongly recommend that this should not be possible.  Derived qualifications should
be based on the original substantive qualifications obtained by study or examination,
and if an actuary, having obtained derived membership in one country on the basis of
his or her home qualifications, moves to a third country, the second derived
membership should be based on the original home qualification, and not on the first
derived membership.  We consider that this distinction can reasonably be made, so that
an actuary who has acquired derived membership in one host Association has not, in
this respect, identical rights to members for whom the membership is a home one.

10. What about actuaries who are not nationals of a “qualifying country” (an EU
Member State, Iceland, Norway or Switzerland)?
The Directives only apply to actuaries who are citizens of Member States (or of those
States party to the European Economic Area Agreement of May 1992).  The Agreement
does not mention nationality, but we consider that there is no obligation on an
Association to accept a migrant actuary who is a member of one of the subscribing
Associations, but who is not a citizen of an EU or EEA Member State or Switzerland.
While Associations are free to accept such an actuary if they wish, we consider that
they should be quite free to refuse membership to those who are not EU, EEA or Swiss
nationals.

11. Can an Association require a migrant actuary to be residing in the host country?
We believe that this would be against the terms of the Directives, and is certainly
against the spirit of the European Union.  Any EU national is now free to live in one EU
country and work or provide services in another, whether just across a border or at
some distance.  Further, the Agreement envisages the possibility of an actuary
providing services on only a part-time basis in any one country (see the next question).

12. Can an Association make any stipulations about the language skills of an
applicant?
We believe that this too would be against the terms of the Directives and would be
against the spirit of the European Union.  But it might well be a breach of that part of the
relevant Code of Conduct, which requires that an actuary shall ensure that he or she
only undertakes duties for which he or she has the relevant current knowledge and
experience, if an actuary does not have language skills that enable him or her to acquire
that knowledge.
13. What does “provides actuarial services on a regular basis” mean?
The purpose of this phrase is clear, but the definition is difficult.  We consider that any
actuary who undertakes statutory duties, such as statutory certification, in a host
country should certainly be strongly encouraged to apply for membership of the host
Association, and in many circumstances he or she may need to do so in order to carry
out those statutory duties.  In other cases an actuary may simply provide advice in a
host country, without carrying out statutory duties.  We recommend that an actuary who
repeatedly or regularly spends, of his or her working time, at least 10% in the host
country working on actuarial business connected with that country should apply to
become a member of the host Association.  But a single assignment, lasting, even
intensively, no more than a few weeks or a small number of months, would not in itself
involve application to the host Association.  Indeed, since an application might well take
several weeks or months to be accepted, it would be a waste of time to make an
application if the connection with the host country were to cease almost as soon as the
application had been accepted.
14. What should happen if an actuary disobeys the Code of Conduct of his or her
host Association?
If a migrant actuary has become a member of the host Association of the country in
which he or she is working, and does not act in accordance with the Rules to be obeyed
in the host country, we recommend that steps need to be taken to correct this
professional misbehaviour in the host country.  We consider that the migrant actuary
should be subject to the same disciplinary procedures as apply to “home” members.  If
the actuary has not joined the host Association, the question of discipline should be
referred to the home Association.
But “punishment” in the host country may not be sufficient, because the actuary
concerned has not only failed to obey the rules of the host Association, but has also not
acted in conformity with his or her home Association’s requirement, accepted in the
Agreement, for its members to behave according to the Code of Conduct of the host
Association in respect of actuarial services provided in the host country.
We therefore recommend to Associations that they should consider invoking disciplinary
procedures against any member who has violated the Code of Conduct and been
punished by a host Association, because of the mere fact of the damage done to the
reputation of his or her home Association.  We consider that this should apply whatever
the home Association’s opinion about the content of the rules that may have been
breached; it should not be a defence against invoking the disciplinary procedures to
argue that the misconduct in the host country would not have been misconduct
according to the rules of the home Association if the offence had been committed in the
home country.
15. What action should a host Association take in the event of professional
misconduct in a home country?
If an actuary were to disobey the Code of Conduct of his or her home Association and
be punished by suspension from the home Association or cancellation of membership,
then we strongly recommend that any host Association with which that actuary has a
derived membership should also suspend him or her or cancel his or her derived
membership as appropriate, or invoke the local disciplinary procedures.
We recommend that, in all cases of misconduct, the principle should be that “an offence
against one Association is an offence against all”.
16. How should Associations deal with the disclosure of misconduct/disciplinary
matters?
It is incumbent on both the home Association and the host Association to notify the
other if an actuary is shown to have committed a breach of the Code of Conduct of that
Association.  In particular, a host Association will wish to know if a visiting actuary
seeking membership under the Mutual Recognition Agreement is, or has been, subject
to any disciplinary measures by his home Association or elsewhere.  This is a delicate
area, which may be subject to data protection or privacy legislation.  The following
principles are recommended:
•  No information should be passed between associations in any circumstances
where a member has been cleared of any charges under a disciplinary
procedure;
•  When a migrant actuary applies to join a host association, the host
Association should ask him/her whether he/she has ever been found guilty of
misconduct by the professional discipline scheme of any other professional
body in any country; at the same time, the host Association should request
information from the home Association on any disciplinary measures against
the individual.  Note that any information exchange in this matter should be
subject to the limits imposed by the legislation on data protection or privacy
protection, in principle in both the countries where the information is given
and where it is received
•  Where an Association makes a public statement (in a journal or otherwise)
about a member who has been found guilty of misconduct, that statement
should be made available to all other associations in the Groupe Consultatif
(including a list of those so found in the past);
•  Where an Association does not currently make that information public, it
should consider whether it has powers to do so under the laws of its country
(in the light, if appropriate, of the EU Services Directive) and, if so, take steps
to arrange to inform the other associations in the Groupe when members are
found guilty (including a list of those so found in the past);

The implementation of many of these recommendations requires communication between
Associations.  For example, if a member who has acquired a derived membership allows
his or her home membership to lapse, then the home Association should be under an
obligation to notify any host Association of which that member has acquired derived
membership.  In order that it can do this, it is necessary for any host Association to notify
the home Association of the granting of a derived membership, and of when it lapses or is
cancelled.  I hope that these recommendations and observations from the Groupe are of
assistance to your Association
Yours sincerely
Chris Daykin
Chairman

Diferenciación actuarial

“… y a mí me llamaron para hacer una supervisión, que yo las cobraba a 500 euros pero me dijeron, oye, que paga la empresa, que paga la empresa,… y entonces tres mil. Pero es un lío, porque claro, el tal lo ha hablao con el otro y han hecho un acuerdo, y yo les digo pero esto está mal, esto no puede ser, y ellos, como ya tienen lo suyo, pues… y yo le digo eh!, y él me dice ah!, y… para que vean ustedes como son las… y bueno, si me pusiera a hablar… yo por esto no hago supervisiones, porque ya está todo pactado… está todo mal… ¿ustedes se creen que uno se puede jubilar y cobrar lo mismo que cuando estaba asalariado? no, ¿verdad? pero todo esto ya está pactao… Lo que no pueden hacer es firmar, claro, hay que ver que las cosas están bien, y si no lo están no se puede firmar, o firmar por firmar, o sea, ser un firmón, que estás ahí sentao y venga, ni te lo miras, que hay muchos por ahí que… porque luego si pasa algo el problema es suyo, y mío, y del otro, y de todos,… y yo llamé a Madrid por eso, y les decía, (se ríe), les decía, oye pero mira lo que están haciendo estos… y me dicen, uy, esto lo tiene que hablar con el supervisor yo no,… y yo pregunté ¿y dónde está el supervisor? pásame con él… uy, no está… y luego hablé con él, y me dice que no quiere saber nada. O sea, para que vean que… te pasan el mochuelo pero ya está todo… está todo…

[...]

… este y el otro son lo mismo, no hay diferencias, bueno, hay una diferencia… que es que no hay diferencias.”

Franquicias estocásticas

Un documento genial de actuarios.org, explica las franquicias de una forma muy pedagógica, desde el comportamiento de las funciones de distribución escogidas (muy pedagógico) hasta cómo programarlo en VBA.

Y sin errores al resolver las integrales!!!!

http://www.actuarios.org/espa/anales/2005/art%20127-199.pdf

Problemas actuariales avanzados III

El profe: ¿cómo se calculan los años bisiestos?
…
Personaje 1º: cuando febrero tiene 29 días.
El profe: sí, claro, pero cómo se sabe qué año va a ser bisiesto?
…
Personaje 2º: cada 4 años.
El profe: Bueno, coges el año y si lo puedes dividir por 4 entonces es un año bisiesto, excepto si es el primero del siglo, que entonces tiene que ser divisible por cuatrocientos.
(…)

J: Realmente todos los números son divisibles por 4.

Corolario actuarial: todos los años son bisiestos.