Analysis of a Degenerate Parabolic Variational Inequality with Gradient Constraints from Optimal Investment and Consumption with Transaction Costs

22 Pages Posted: 8 Jan 2007

See all articles by Min Dai

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Lishang Jiang

Tongji University - Institute of Mathematics

Fahuai Yi

South China Normal University - Department of Math

Date Written: January 4, 2007

Abstract

This paper is concerned with a degenerate parabolic variational inequality with gradient constraints arising from an optimal investment and consumption problem with proportional transaction costs. We are most interested in the resulting free boundaries that correspond to the optimal trading strategies. Under a reasonable technical condition, we present a complete analysis of the smoothness of solution and the behaviors of free boundaries.

Keywords: optimal investment and consumption, transaction costs, finite horizon, free boundaries, variational inequality, gradient constraints

Suggested Citation

Dai, Min and Jiang, Lishang and Yi, Fahuai, Analysis of a Degenerate Parabolic Variational Inequality with Gradient Constraints from Optimal Investment and Consumption with Transaction Costs (January 4, 2007). Available at SSRN: https://ssrn.com/abstract=955465 or http://dx.doi.org/10.2139/ssrn.955465

Min Dai (Contact Author)

National University of Singapore (NUS) - Department of Mathematics ( email )

Singapore

Lishang Jiang

Tongji University - Institute of Mathematics ( email )

1239 Siping Road
Shanghai, 200092
China

Fahuai Yi

South China Normal University - Department of Math ( email )

Guangzhou, 510631
China

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