Abstract
The theory of risk measurement has been extensively developed over the past ten years or so, but there has been comparatively little effort devoted to using this theory to inform portfolio choice. One theme of this paper is to study how an investor in a conventional log-Brownian market would invest to optimize expected utility of terminal wealth, when subjected to a bound on his risk, as measured by a coherent law-invariant risk measure. Results of Kusuoka lead to remarkably complete expressions for the solution to this problem. The second theme of the paper is to discuss how one would actually manage (not just measure) risk. We study a principal/agent problem, where the principal is required to satisfy some risk constraint. The principal proposes a compensation package to the agent, who then optimises selfishly ignoring the risk constraint. The principal can pick a compensation package that induces the agent to select the principal’s optimal choice.
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The author gratefully acknowledges support from the Cambridge Endowment for Research in Finance; helpful discussions with Peter Bank, Phil Dybvig, Henrik Hult, Ludger Rüschendorf, and Yuliy Sannikov; and comments from participants in the Cambridge-Princeton conference, September 2008, and seminars at King’s College London, Oxford, Warwick, MAN Investments, and Heriot-Watt.
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Rogers, L.C.G. Optimal and robust contracts for a risk-constrained principal. Math Finan Econ 2, 151–171 (2009). https://doi.org/10.1007/s11579-009-0018-x
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DOI: https://doi.org/10.1007/s11579-009-0018-x