Optimal investment in the presence of intangible assets and collateralized optimal debt ratio in jump-diffusion models

Abstract

This paper studies an investor’s optimal investment, optimal net debt ratio with collateral security and optimal consumption plan in an economy that faces both diffusion and jump risks. The underlying assets are tangible and intangible assets. There have been major challenges of quantifying intangible assets. In this paper, we assume that the price of our intangible asset follows a jump-diffusion process. The tangible asset of the investor is divided into two parts: financial and nonfinancial (fixed) assets. Financial assets are invested into a market that is made up of a riskless asset and multiple risky assets (stocks). The fixed asset and stock prices follow jump-diffusion processes. This paper aim at (1) maximizing the total expected discounted utility of consumption in the infinite time horizon in the presence of both tangible and intangible assets, (2) determining the optimal net debt ratio for an investor in the presence of jumps, (3) determining the effect of intangible assets on the investor’s portfolio and (4) determining the optimal portfolio strategies of an investor who invest in an economy that is exposed to both diffusion and jump risks. This paper obtained the optimal consumption, optimal portfolio strategies and optimal net debt ratio of an investor under some suitable utility functions. We found that the value of the intangible assets depends explicitly on all the market parameters including the production rate, optimal wealth and optimal debt ratio of the investor over time. This implies that any change in the market parameter values, optimal investment, optimal net debt ratio and the production rate will lead to changes in the values of the intangible assets.