We consider optimal consumption and portfolio investment problems of an investor who is interested in maximizing his utilities from consumption and terminal wealth subject to a random inflation in the consumption basket price over time. We consider two cases: (i) when the investor observes the...

We solve an agent's optimization problem of meeting demands for cash over time with cash deposited in bank or invested in stock. The stock pays dividends and uncertain capital gains, and a commission is incurred in buying and selling of stock. We use a stochastic maximum principle to obtain...

We solve an agent's optimization problem of meeting demands for cash over time with cash deposited in bank or invested in stock. The stock pays dividends and uncertain capital gains, and a commission is incurred in buying and selling of stock. We use a stochastic maximum principle to obtain...

We present a sufficient condition for a feedback Stackelberg equilibrium of a stochastic differential game on an infinite horizon. This condition gives rise to a system of elliptic partial differential equations involving a static Stackelberg game at the level of Lagrangian. As an example, we...

Inventory inaccuracy is common at retailers. At many retailers, a cash register records incoming orders and outgoing sales, but not the demand or the shrinkage. The shrinkage refers to spoilage or pilferage of inventory. The demand differs from the sales in the periodic-review lost-sales...

We develop a general methodology for a partially observed stochastic control problem. The dynamics is governed by a discrete-time Markov process. We describe an application to an inventory system with possibility of shrinkage, and introduce unnormalized conditional probabilities to transform the...