Optimizing Terminal Wealth with Static Derivatives and Dynamic Stocks

Summary

The paper frames an investor’s problem as maximizing expected utility of wealth at a future horizon. It combines two kinds of positions: derivatives chosen once at the start and stock holdings adjusted dynamically over time. The setup allows the derivative position to remain fixed while the stock strategy responds as the market evolves.

The analysis is stated in a general semimartingale framework, with utility defined for positive wealth. The excerpt describes the problem formulation but gives no solution method, results, examples, or empirical evidence. It therefore establishes the scope and assumptions rather than showing how to implement an optimal strategy. The usefulness of any conclusions would depend on details absent here, including the precise utility function, derivative payoffs, trading constraints, and market assumptions.

Key ideas

• The objective is to maximize expected utility of terminal wealth.
• Derivative positions are selected at the initial time and held static.
• Stock positions can be adjusted dynamically during the investment horizon.
• The framework uses a general semimartingale market model and positive-wealth utility.

Tags

# Optimal Investment with Stocks and Derivatives


# Optimal Investment with Stocks and Derivatives









This paper studies the problem of maximizing expected utility from terminal wealth combining a static position in derivative securities, which we assume can be traded only at time zero, with a traditional dynamic trading strategy in stocks. We work in the framework of a general semi-martingale model and consider a utility function defined on the positive real line.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.