Investment-consumption models with transaction fees and Markov-chain parameters
SIAM Journal on Control and Optimization
Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
Optimal Consumption and Portfolio with Both Fixed and Proportional Transaction Costs
SIAM Journal on Control and Optimization
Weak Dynamic Programming Principle for Viscosity Solutions
SIAM Journal on Control and Optimization
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This work focuses on optimal switching with constraints. Our motivation stems from utility maximization of an indivisible market. The dynamic programming approach is used; the value function is characterized as the unique viscosity solution of a quasi-variational inequality. The unbounded domain introduces new challenges. By studying the sample paths of the diffusion at the boundary, a sufficient condition for the continuity of the value function is provided, yielding the desired characterization. Not only are the results of this work applicable to the utility maximization problem, but also they can be used for general optimal switching problems with finite regimes.