Risk/Arbitrage Strategies: An Application to the Pricing and Hedging of Dual Trigger Stop Loss Treaties

Abstract. Asset/Liability management, optimal fund design and optimal portfolio selection have been key issues of interest to the (re)insurance and investment banking communities, respectively, for some years especially in the design of advanced risk transfer solutions for clients in the Fortune 500 group of companies. The new concept of limited risk arbitrage investment management in a diffusion type securities and derivatives market introduced in our papers Risk/Arbitrage Strategies: A New Concept for Asset/Liability Management, Optimal Fund Design and Optimal Portfolio Selection in a Dynamic, Continuous-Time Framework Part I: Securities Markets and Part II: Securities and Derivatives Markets, AFIR 1997, Vol. II, p. 543, is immediately applicable to ALM, optimal fund design and portfolio selection problems in the investment banking and life insurance areas. The main quantities of practical interest (i.e., the optimal LRA asset allocation, etc.) can be derived by essentially solving a (quasi-) linear partial differential equation of the second order (e.g., by using a finite difference approximation with locally uniform convergence properties). Similarly, in our more sophisticated impluse control approach to modelling the RCLL risk portfolio dynamics of a large, internationally operating (re)insurer with considerable (“catastrophic”) non-life exposures, the optimal portfolio strategies can be determined numerically by using an efficient Markov chain approximation scheme, i.e., essentially the same (formal) finite difference techniques (with weak convergence properties), see Part III: A Risk/Arbitrage Pricing Theory and Part IV: An Impulse Control Approach to Limited Risk Arbitrage of the above mentioned publication series and also the paper Baseline for Exchange Rate Risks of an International Reinsurer, AFIR 1996, Vol. I, p. 395. However, in many practical applications there are even simpler numerical solution techniques, see Part V: A Guide to Efficient Numerical Implementations of the above mentioned publication series. We present here such an alternative lattice-based methodology that can be used to price and hedge dual trigger stop loss treaties (and, more generally, any claim contingent on financial and (re)insurance markets variables) as an example.