Terminal wealth maximization under drift uncertainty
Uğurlu K.
2025Taylor and Francis Ltd.
Optimization
2025#74Issue 71743 - 1761 pp.
We study the portfolio optimization problem of an investor seeking to maximize his terminal wealth. The portfolio is composed of one risky asset, a stock, and one riskless asset, a bond. We assume there is Knightian uncertainty on the stochastic drift term representing the long-term growth rate of the risky asset whose values are not necessarily bounded. We further assume that the investor has a prior estimate about the drift term and quantifies the diffidence of the investor in his prior about the mean. It is assumed that the investor has a logarithmic or power utility. Explicit solutions with unbounded, stochastic and uncertain drift terms have been retrieved. Numerical illustrations revealing the effect of risk awareness and uncertainty on the value function and optimal parameters are also presented.
Knightian uncertainty , mathematical finance , risk management , robust optimization , utility maximization
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Department of Mathematics, Nazarbayev University, Astana, Kazakhstan
Department of Mathematics
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