“Cash Flow Matching: A Risk Management Approach”, Garud Iyengar and Alfred Ka Chun Ma,July, 2009

Abstract

Consider a discrete-time risk model in which the insurer is allowed to invest a proportion of its wealth in a risky stock and keep the rest in a risk-free bond. Assume that the claim amounts within individual periods follow an autoregressive process with heavy-tailed innovations and that the log-returns of the stock follow another auto regressive process, independent of the former one. We derive an asymptotic formula for the finite-time ruin probability and propose a hybrid method, combining simulation with asymptotics, to compute this ruin probability more efficiently. As an application, we consider a portfolio optimization problem in which we determine the proportion invested in the risky stock that maximizes the expected terminal wealth subject to a constraint on the ruin probability.     

Probability and Statistics Applied to the Practice of Financial Risk Management: The Case of J.P. Morgan's RiskMetrics™

This work describes applications of probability and statistics in RiskMetrics, J.P. Morgan's methodology for quantifying market risk. The methodology implements an analytical approach to financial risk in trading, arbitrage, and investment based on the statistics of market moves in equities, bonds, currencies and commodities. The public unveiling of RiskMetrics in October of 1994 attracted widespread interest among regulators, competing financial institutions, investment managers, and corporate treasurers, while the available technical documentation offers us a unique opportunity for informed statistical research on the theory and practice of financial risk management. For the purpose of identifying problems for further research, this discussion focuses on five applications of statistics in RiskMetrics, which range from data analysis of daily returns and locally Gaussian processes to stochastic volatility models and Itô processes for the term structure of interest rates. Another important theme of this discussion, however, is devoted to attracting statisticians to the study of financial risk management and developing the foundations for collaborative work with financial economists and practicing risk managers. For this reason, this is also an expository document that touches several areas of active statistical research with applications to problems of risk management.