Skip to content
All library documents

Defining Terminal Wealth in Finite-Horizon Asset Pricing

Article Quant Q&A · Author: Ignacio Canabal
Read the original

Summary

The question examines how to define terminal wealth in a finite-horizon asset-pricing model. Agents have exponential utility and consume only in the final period, so their objective is to maximize wealth at the horizon. Earlier wealth can be described through portfolio returns and the value of holdings, but the author is uncertain how to price the final portfolio when the model ends and there is no subsequent period to reveal demand.

The document presents the modeling problem but offers no proposed terminal condition, answer, or evidence. It highlights that a finite-horizon setup needs an explicit rule for valuing assets at the endpoint, such as a specified terminal payoff or exogenous liquidation value; without one, the final portfolio’s price is not determined by the described dynamics alone. This is a conceptual question about market clearing and terminal conditions, rather than a developed pricing method.

Key ideas

  • The model has exponential-utility agents who consume only at the horizon.
  • The objective is to maximize final wealth in a finite-horizon asset-pricing setting.
  • Prices before the horizon depend on portfolio returns and demand for the assets.
  • The question leaves the final portfolio’s valuation rule unspecified.
  • A terminal condition is needed to determine how final holdings are valued.

Tags

Multi-assetPortfolio constructionStatistics
Full text
# Terminal wealth in multiperiod asset pricing?


# Terminal wealth in multiperiod asset pricing?












I am studying an asset pricing problem and I am having a tough time using finite horizon because I cannot properly define the terminal wealth.

I consider agents with exponential utility, who can consume only at the last period. So, the objective is to maximize terminal wealth at time T. I see how wealth at time n<T will be the returns on the portfolio held plus the price at n of that portfolio, and that price depends on the demand at time n. How to define the price of the final portfolio held? Since the model stops at T we cannot know what the future demand will be or know what the final price is, unless we add more periods to model.

Thank you !

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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