On the Optimal Wealth Process in a Log-normal Market: Applications to Risk Management

Phillip Monin () and Thaleia Zariphopoulou ()
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Phillip Monin: Office of Financial Research
Thaleia Zariphopoulou: The University of Texas at Austin

No 14-01, Staff Discussion Papers from Office of Financial Research, US Department of the Treasury

Abstract: The theory of portfolio choice holds that investors balance risk and reward in their investment decisions. We explore the relationship between investors' attitudes towards taking risk and their objectives for managing the risk they take on. Working in a classical theoretical model, we calculate the distribution and density functions of an investor's optimal wealth process and prove new mathematical results for these functions under general risk preferences. By applying our results to a constant relative risk aversion investor who has a targeted value at risk or expected shortfall at a given future time, we are able to infer the investor's risk preferences and prescribe how to invest to achieve the desired goal. Then, drawing analogies to the option greeks, we define and derive closed-form expressions for "portfolio greeks," which measure the sensitivities of an investor's optimal wealth to changes in the cumulative excess stock return, time, and market parameters. Like option greeks, portfolio greeks can be used in the risk management of investors' portfolios.

Keywords: expected utility; Merton problem; value at risk (VaR); expected shortfall; portfolio greeks (search for similar items in EconPapers)
Pages: 34 pages
Date: 2014-07-18
New Economics Papers: this item is included in nep-rmg and nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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