DYNAMIC COHERENT ACCEPTABILITY INDICES AND THEIR APPLICATIONS TO FINANCE

Tomasz R. Bielecki · Igor Cialenco · Zhao Zhang

39 citations0/0 files storedMathematical Finance

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Risk and Portfolio Optimization Stochastic processes and financial applications Financial Risk and Volatility Modeling

Abstract

In this paper, we present a theoretical framework for studying coherent acceptability indices (CAIs) in a dynamic setup. We study dynamic CAIs (DCAIs) and dynamic coherent risk measures (DCRMs), and we establish a duality between them. We derive a representation theorem for DCRMs in terms of a so‐called dynamically consistent sequence of sets of probability measures. Based on these results, we give a specific construction of DCAIs. We also provide examples of DCAIs, both abstract and also some that generalize selected classical financial measures of portfolio performance.

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References

1999Coherent Measures of Risk 1966Mutual Fund Performance 2002Convex measures of risk and trading constraints 1994Performance Measurement in a Downside Risk Framework 2002Coherent Risk Measures on General Probability Spaces 2004Stochastic Finance 2002Putting order in risk measures 2001On law invariant coherent risk measures

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2013Time consistency of dynamic risk measures in markets with transaction costs 2013Acceptability indexes via $$g$$ -expectations: an application to liquidity risk

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