This paper studies a non-concave optimization problem under a Value-at-Risk (VaR) or an Expected Shortfall (ES) constraint . The non-concavity of the problem stems from the non-linear payoff structure of the optimizing investor . We obtain the closed-form optimal wealth with an ES constraint as well as with a VaR constraint respectively, and explicitly calculate the optimal trading strategy for constant relative risk aversion (CRRA) utility functions. In our non-concave optimization problem, we find that with a not too strict regulation for any VaR-constraint with an arbitrary risk level, there exists an ES-constraint leading to the same investment strategy, which shows on some level the ineffectiveness of the ES-based  regulation  . This differs from the conclusion drawn in Basak and Shapiro ( 2001 ) for the concave optimization problem, where VaR and ES lead to different solutions and ES provides a better loss protection.
This paper studies an optimal asset allocation problem for a surplus-driven financial institution facing a Value-at-Risk (VaR) or an Expected Shortfall (ES) constraint corresponding to a non-concave optimization problem under constraints . We obtain the closed-form optimal wealth with the ES constraint as well as with the VaR constraint respectively, and explicitly calculate the optimal trading strategy for constant relative risk aversion (CRRA) utility functions. We find that both VaR and ES-based regulation can effectively reduce the probability of default for a surplus-driven financial institution. However, the liability holders' benefits cannot be fully protected under either VaR- or ES-based regulation. In addition, we show that the VaR and ES-based regulation can induce the same optimal portfolio choice for a surplus-driven financial institution . This differs from the conclusion drawn in Basak and Shapiro 2001 where the financial institution aims at maximizing the expected utility of the total assets, and ES provides better loss protection.
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a non-concave optimization problem under a
an optimal asset allocation problem for a surplus-driven financial institution facing a
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. The non-concavity of the problem stems from the non-linear payoff structure of the optimizing investor
corresponding to a non-concave optimization problem under constraints
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In our non-concave optimization problem, we find that with a not too strict regulation for any VaR-constraint with an arbitrary risk level, there exists an ES-constraint leading to the same investment strategy, which shows on some level the ineffectiveness of the
We find that both VaR and ES-based regulation can effectively reduce the probability of default for a surplus-driven financial institution. However, the liability holders' benefits cannot be fully protected under either VaR- or
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regulation. In addition, we show that the VaR and ES-based
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can induce the same optimal portfolio choice for a surplus-driven financial institution
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(
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) for the concave optimization problem, where VaR and ES lead to different solutions and ES provides a
where the financial institution aims at maximizing the expected utility of the total assets, and ES provides