Dual-goal portfolio optimization reveals growth crowding-out and deadline pressure effects plus non-monotonic value functions arising from forced funding interactions between random and fixed deadlines.
Goal-based portfolio selection with mental accounting
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abstract
We present a continuous-time portfolio selection framework that reflects goal-based investment principles and mental accounting behavior. In this framework, an investor with multiple investment goals constructs separate portfolios, each corresponding to a specific goal, with penalties imposed on fund transfers between these goals, referred to as mental costs. By applying the stochastic Perron's method, we demonstrate that the value function is the unique constrained viscosity solution of a Hamilton-Jacobi-Bellman equation system. Numerical analysis reveals several key features: the free boundaries exhibit complex shapes with bulges and notches; the optimal strategy for one portfolio depends on the wealth level of another; investors must diversify both among stocks and across portfolios; and they may postpone reallocating surplus from an important goal to a less important one until the former's deadline approaches.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Causal optimal transport value between finite-state Markov source and diffusion target is characterized by a nonlinear parabolic master equation on enlarged state space and shown equivalent to Kushner-Stratonovich filtering control with zero-mean condition and state-constrained control.
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Portfolio Choice with Competing Precautionary and Accumulation Goals
Dual-goal portfolio optimization reveals growth crowding-out and deadline pressure effects plus non-monotonic value functions arising from forced funding interactions between random and fixed deadlines.
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Analytical Approach to Continuous-Time Causal Optimal Transport
Causal optimal transport value between finite-state Markov source and diffusion target is characterized by a nonlinear parabolic master equation on enlarged state space and shown equivalent to Kushner-Stratonovich filtering control with zero-mean condition and state-constrained control.