### Abstract

Solvency regulations require financial institutions to hold initial capital so that ruin is a rare event. An important practical problem is to estimate the regulatory capital so the ruin probability is at the regulatory level, typically with less than 0.1% over a finite-Time horizon. Estimating probabilities of rare events is challenging, since naive estimations via direct simulations of the surplus process is not feasible. In this paper, we present a stratified sampling algorithm for estimating finite-Time ruin probabilities. We further introduce a sequence of measure changes to remove the pathwise discontinuities of the estimator, and compute unbiased first and second-order derivative estimates of the finite-Time ruin probabilities with respect to both distributional and structural parameters. We then estimate the regulatory capital and its sensitivities. These estimates provide information to insurance companies for meeting prudential regulations as well as designing risk management strategies. Numerical examples are presented for the classical model, the Sparre Andersen model with interest and the periodic risk model with interest to demonstrate the speed and efficacy of our methodology.

Original language | English |
---|---|

Pages (from-to) | 431-467 |

Number of pages | 37 |

Journal | ASTIN Bulletin |

Volume | 46 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 May 2016 |

### Keywords

- Monte Carlo
- risk-based capital
- ruin probabilities
- Sensitivity analysis

### Cite this

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*ASTIN Bulletin*, vol. 46, no. 2, pp. 431-467. https://doi.org/10.1017/asb.2016.5

**The efficient computation and the sensitivity analysis of finite-time ruin probabilities and the estimation of risk-based regulatory capital.** / Joshi, Mark S.; Zhu, Dan.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - The efficient computation and the sensitivity analysis of finite-time ruin probabilities and the estimation of risk-based regulatory capital

AU - Joshi, Mark S.

AU - Zhu, Dan

PY - 2016/5/1

Y1 - 2016/5/1

N2 - Solvency regulations require financial institutions to hold initial capital so that ruin is a rare event. An important practical problem is to estimate the regulatory capital so the ruin probability is at the regulatory level, typically with less than 0.1% over a finite-Time horizon. Estimating probabilities of rare events is challenging, since naive estimations via direct simulations of the surplus process is not feasible. In this paper, we present a stratified sampling algorithm for estimating finite-Time ruin probabilities. We further introduce a sequence of measure changes to remove the pathwise discontinuities of the estimator, and compute unbiased first and second-order derivative estimates of the finite-Time ruin probabilities with respect to both distributional and structural parameters. We then estimate the regulatory capital and its sensitivities. These estimates provide information to insurance companies for meeting prudential regulations as well as designing risk management strategies. Numerical examples are presented for the classical model, the Sparre Andersen model with interest and the periodic risk model with interest to demonstrate the speed and efficacy of our methodology.

AB - Solvency regulations require financial institutions to hold initial capital so that ruin is a rare event. An important practical problem is to estimate the regulatory capital so the ruin probability is at the regulatory level, typically with less than 0.1% over a finite-Time horizon. Estimating probabilities of rare events is challenging, since naive estimations via direct simulations of the surplus process is not feasible. In this paper, we present a stratified sampling algorithm for estimating finite-Time ruin probabilities. We further introduce a sequence of measure changes to remove the pathwise discontinuities of the estimator, and compute unbiased first and second-order derivative estimates of the finite-Time ruin probabilities with respect to both distributional and structural parameters. We then estimate the regulatory capital and its sensitivities. These estimates provide information to insurance companies for meeting prudential regulations as well as designing risk management strategies. Numerical examples are presented for the classical model, the Sparre Andersen model with interest and the periodic risk model with interest to demonstrate the speed and efficacy of our methodology.

KW - Monte Carlo

KW - risk-based capital

KW - ruin probabilities

KW - Sensitivity analysis

UR - http://www.scopus.com/inward/record.url?scp=84960090570&partnerID=8YFLogxK

U2 - 10.1017/asb.2016.5

DO - 10.1017/asb.2016.5

M3 - Article

VL - 46

SP - 431

EP - 467

JO - ASTIN Bulletin

JF - ASTIN Bulletin

SN - 0515-0361

IS - 2

ER -