The Robust Computation and the Sensitivity Analysis of Finite-Time Ruin Probabilities and the Estimation of Risk-Based Regulatory Capital

2014 ◽  
Author(s):  
Mark S. Joshi ◽  
Dan Zhu
Keyword(s):  
Sensitivity Analysis ◽  
Finite Time ◽  
Ruin Probabilities ◽  
Regulatory Capital ◽  
Robust Computation ◽  
Estimation Of Risk

THE EFFICIENT COMPUTATION AND THE SENSITIVITY ANALYSIS OF FINITE-TIME RUIN PROBABILITIES AND THE ESTIMATION OF RISK-BASED REGULATORY CAPITAL

2016 ◽  
Vol 46 (2) ◽  
pp. 431-467
Author(s):  
Mark S. Joshi ◽  
Dan Zhu
Keyword(s):  
Finite Time ◽  
Risk Model ◽  
Structural Parameters ◽  
Classical Model ◽  
Management Strategies ◽  
Rare Event ◽  
Insurance Companies ◽  
Ruin Probabilities ◽  
Efficient Computation ◽  
Regulatory Capital

AbstractSolvency 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.

Uniform estimate on finite time ruin probabilities with random interest rate

2010 ◽  
Vol 30 (3) ◽  
pp. 688-700 ◽  
Author(s):  
Ming Ruixing ◽  
He Xiaoxia ◽  
Hu Yijun ◽  
Liu Juan
Keyword(s):  
Interest Rate ◽  
Finite Time ◽  
Uniform Estimate ◽  
Ruin Probabilities
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