Portfolio optimization under the Value-at-Risk constraint

Traian A. Pirvu

Quantitative Finance, 2007, vol. 7, issue 2, 125-136

Abstract: In this paper we analyse the effects arising from imposing a Value-at-Risk constraint in an agent's portfolio selection problem. The financial market is incomplete and consists of multiple risky assets (stocks) plus a risk-free asset. The stocks are modelled as exponential Brownian motions with random drift and volatility. The risk of the trading portfolio is re-evaluated dynamically, hence the agent must satisfy the Value-at-Risk constraint continuously. We derive the optimal consumption and portfolio allocation policy in closed form for the case of logarithmic utility. The non-logarithmic CRRA utilities are considered as well, when the randomness of market coefficients is independent of the Brownian motion driving the stocks. The portfolio selection, a stochastic control problem, is reduced, in this context, to a deterministic control one, which is analysed, and a numerical treatment is proposed.

Keywords: Value-at-Risk (VaR); Utility functions; Portfolio optimization; Portfolio theory; Portfolio management (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (11)

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DOI: 10.1080/14697680701213868

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