# Approximation of the probability of insolvability of a portfolio

Mathematica Applicanda (2005)

- Volume: 33, Issue: 47/06
- ISSN: 1730-2668

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topRobert Pusz, and Tomasz Rolski. "Approximation of the probability of insolvability of a portfolio." Mathematica Applicanda 33.47/06 (2005): null. <http://eudml.org/doc/292953>.

@article{RobertPusz2005,

abstract = {The authors review and criticize different approaches for calculations of ruin probabilities in one or multiperiod life insurance portfolios. They claim that precise calculations are time-consuming and in some cases (especially in the multiperiod ones) are practically inaccessible even if theoretical formulae are available. The reviewer considers that, because parameters of any such model must be estimated somehow, then precision in calculations cannot be achieved. For example, the authors assume a constant interest rate, which is not precisely the best way of doing things for the multiperiod model, and the precision must be lost anyway. Particularly, the authors show that the use of the central limit theorem is not appropriate; errors are large. The precise recursive method is difficult to perform for a large portfolio. The authors propose the importance of the Monte Carlo sampling method instead of the crude one. Their estimations are based on some probabilistic inequalities such as a version of Chernoff's (saddle point), also analyzed by S. Asmussen [Stochastic simulation with a view toward stochastic processes, Univ. Aarhus, Aarhus, 1999; Zbl 0981.65013], and are related to the approximation from D. Blackwell and J. L. Hodges, Jr. [Ann. Math. Statist. 30 (1959), 1113–1120; MR0112197].},

author = {Robert Pusz, Tomasz Rolski},

journal = {Mathematica Applicanda},

keywords = {Finance, portfolios, investment; Approximations to distributions (nonasymptotic)},

language = {eng},

number = {47/06},

pages = {null},

title = {Approximation of the probability of insolvability of a portfolio},

url = {http://eudml.org/doc/292953},

volume = {33},

year = {2005},

}

TY - JOUR

AU - Robert Pusz

AU - Tomasz Rolski

TI - Approximation of the probability of insolvability of a portfolio

JO - Mathematica Applicanda

PY - 2005

VL - 33

IS - 47/06

SP - null

AB - The authors review and criticize different approaches for calculations of ruin probabilities in one or multiperiod life insurance portfolios. They claim that precise calculations are time-consuming and in some cases (especially in the multiperiod ones) are practically inaccessible even if theoretical formulae are available. The reviewer considers that, because parameters of any such model must be estimated somehow, then precision in calculations cannot be achieved. For example, the authors assume a constant interest rate, which is not precisely the best way of doing things for the multiperiod model, and the precision must be lost anyway. Particularly, the authors show that the use of the central limit theorem is not appropriate; errors are large. The precise recursive method is difficult to perform for a large portfolio. The authors propose the importance of the Monte Carlo sampling method instead of the crude one. Their estimations are based on some probabilistic inequalities such as a version of Chernoff's (saddle point), also analyzed by S. Asmussen [Stochastic simulation with a view toward stochastic processes, Univ. Aarhus, Aarhus, 1999; Zbl 0981.65013], and are related to the approximation from D. Blackwell and J. L. Hodges, Jr. [Ann. Math. Statist. 30 (1959), 1113–1120; MR0112197].

LA - eng

KW - Finance, portfolios, investment; Approximations to distributions (nonasymptotic)

UR - http://eudml.org/doc/292953

ER -

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