In this paper we analyze how an individual should optimally invest in human capital when he also has financial wealth. We treat the individual’s option to take more education as expansion options and apply real option analysis. We characterize the individual’s optimal consumption strategy and portfolio weights. The individual has a demand for hedging financial risk, labor income risk, and also ...

We describe some stochastic control problems in financial engineering arising from the need to find investment strategies to optimize some goal. Typically, these problems are characterized by nonlinear Hamilton-Jacobi-Bellman partial differential equations, and often they can be reduced to linear PDEs with the Legendre transform of convex duality. One situation where this cannot be achieved is ...

This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. We rely on the dynamic programming approach to solve the optimization problem. The properties of the value function, particularly the homogeneity, are used to reduce the HJB equation by one dimension. Furt...

In this paper we consider an agent on a financial market who can trade with an uncertain time horizon by investing in risky stocks and a risk-free bond. He aims at maximizing the utility he draws from his final wealth measured by some utility function. We obtain a sufficient and necessary condition for the optimality, which gives an explicit expression for the optimal strategies as solutions of...

This paper investigates the optimal time-consistent policies of an investment-reinsurance problem and an investment-only problem under the mean-variance criterion for an insurer whose surplus process is approximated by a Brownianmotionwith drift. The financial market considered by the insurer consists of one risk-free asset and multiple risky assets whose price processes follow geometric Browni...

We consider the problem of optimal investment and consumption when the investment opportunity is represented by a hedge-fund charging proportional fees on profit. The value of the fund evolves as a geometric Brownian motion and the performance of the investment and consumption strategy is measured using discounted power utility from consumption on infinite horizon. The resulting stochastic cont...

We design an optimal strategy for investment in a portfolio of assets subject to a multiplicative Brownian motion. The strategy provides the maximal typical long-term growth rate of investor’s capital. We determine the optimal fraction of capital that an investor should keep in risky assets as well as weights of different assets in an optimal portfolio. In this approach both average return and ...

Segmentation is a core strategy in modern marketing, and age-specific segmentation based on the age of the consumers is very common in practice. Age-specific segmentation enables the change of the segments composition during time and can be studied only by means of dynamic advertising models. Here we assume that a firm wants to optimally promote and sell a single product in an age-segmented mar...

We study the problem of optimal investment by embedding it in the general conjugate duality framework of convex analysis. This allows for various extensions to classical models of liquid markets. In particular, we obtain a dual representation for the optimum value function in the presence of portfolio constraints and nonlinear trading costs that are encountered e.g. in modern limit order market...

An agent can invest in a high—yield bond and a low—yield bond, holding either long or short positions in either asset. Any movement of money between these two assets incurs a transaction cost proportional to the size of the transaction. The low—yield bond is liquid in the sense that wealth invested in this bond can be consumed directly without a transaction cost; wealth invested in the high—yie...