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- W2785454311 abstract "We assume that the wealth process $X^u$ is self-financing and generated from the initial wealth by holding a fraction $u$ of $X^u$ in a risky stock (whose price follows a geometric Brownian motion) and the remaining fraction $1-u$ of $X^u$ in a riskless bond (whose price compounds exponentially with interest rate $r in {R}$). Letting $P_{t,x}$ denote a probability measure under which $X^u$ takes value $x$ at time $t,$ we study the dynamic version of the nonlinear optimal control problem $inf_u, Var{t,X_t^u}(X_T^u)$ where the infimum is taken over admissible controls $u$ subject to $X_t^u ge e^{-r(T-t)} g$ and $E{t,X_t^u}(X_T^u) ge beta$ for $ t in [0,T]$. The two constants $g$ and $beta$ are assumed to be given exogenously and fixed. By conditioning on the expected terminal wealth value, we show that the nonlinear problem can be reduced to a family of linear problems. Solving the latter using a martingale method combined with Lagrange multipliers, we derive the dynamically optimal control $u_*^d$ ..." @default.
- W2785454311 created "2018-02-23" @default.
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- W2785454311 date "2018-01-01" @default.
- W2785454311 modified "2023-09-25" @default.
- W2785454311 title "Constrained Dynamic Optimality and Binomial Terminal Wealth" @default.
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- W2785454311 doi "https://doi.org/10.1137/16m1085097" @default.
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