Transversality Conditions for Stochastic Higher-Order Optimality: Continuous and Discrete Time Problems

TL;DR

This paper derives Euler equations and transversality conditions for stochastic higher-order optimization problems in both continuous and discrete time, extending existing economic models to include more complex, realistic scenarios.

Contribution

It provides a general framework for higher-order stochastic optimization, including new transversality conditions and Euler equations applicable to continuous and discrete time models.

Findings

Established Euler equations for higher-order stochastic problems.

Derived transversality conditions for continuous and discrete time.

Applied results to a household maximization model.

Abstract

Higher-order optimization problems naturally appear when investigating the effects of a patent with finite length, as in the pioneering work of Futagami and Iwaisako (2007). In this paper, we establish the Euler equations and transversality conditions necessary for analyzing such higher-order optimization problems. We develop our results for stochastic general reduced-form models and consider cases of both continuous and discrete time. We employ our results to establish the Euler equations and transversality conditions for the simplified household maximization problem in Futagami and Iwaisako (2007).