We consider the optimal investment and consumption problem in a Black–Scholes market, if the target functional is given by expected discounted utility of consumption plus expected discounted utility of terminal wealth. We investigate the behaviour of the optimal strategies, if the relative risk aversion tends to infinity. It turns out that the limiting strategies are: do not invest at all in the stock market and keep the rate of consumption constant!
Grandits P, Summer C (2006) Risk averse asymptotics and the optional decomposition. Teor Veroyatn Primen 51(2): 409–418MathSciNetGoogle Scholar
Karatzas I, Lehoczky JP (1987) Shreve SE Optimal portfolio and consumption decisions for a “small investor” on a finite horizon. SIAM J Control Optim 25(6): 1557–1586MathSciNetMATHCrossRefGoogle Scholar
Ladyženskaja OA, Solonnikov VA, Uraĺceva NN (1967) Linear and quasilinear equations of parabolic type. American Mathematical Society, ProvidenceGoogle Scholar
Merton RC (1969) Lifetime portfolio selection under uncertainty: the continuous time case. Rev Econ Stat 51: 247–257CrossRefGoogle Scholar