Optimal derivatives design under dynamic risk measures

Pauline M. Barrieu · Nicole El Karoui

109 citations0/0 files storedContemporary mathematics - American Mathematical Society

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Risk and Portfolio Optimization Stochastic processes and financial applications Risk Management in Financial Firms

Abstract

We develop a methodology to optimally design a financial issue to hedge non-tradable risk on financial markets. Economic agents assess their risk using monetary risk measure. The inf-convolution of convex risk measures is the key transformation in solving this optimization problem. When agents' risk measures only di#er from a risk aversion coe#cient, the optimal risk transfer is amazingly equal to a proportion of the initial risk.

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References

1971Optimum consumption and portfolio rules in a continuous-time model 2002Convex measures of risk and trading constraints 2002Stochastic Finance: An Introduction in Discrete Time 2000Backward stochastic differential equations and partial differential equations with quadratic growth 1989Optimal replication of contingent claims under transaction costs 2000The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets 1992Equilibrium in a Reinsurance Market 1992The Design of an Optimal Insurance Policy

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