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.

本文研究了面临扩散和跳跃风险的经济体中投资者的最优投资，最优净债务比率和抵押担保以及最优消费计划。标的资产是有形和无形资产。量化无形资产一直存在重大挑战。在本文中，我们假设无形资产的价格遵循跳跃扩散过程。投资者的有形资产分为两部分：金融和非金融（固定）资产。金融资产投资到由无风险资产和多种风险资产（股票）组成的市场中。固定资产和股票价格遵循跳跃扩散过程。本文旨在（1）在有形和无形资产同时存在的情况下，在无限的时间范围内最大化预期的总消费折现效用;（2）在存在跳跃的情况下确定投资者的最佳净债务比率;（3） ）确定无形资产对投资者投资组合的影响，以及（4）确定在暴露于扩散和跳跃风险的经济环境中投资的投资者的最佳投资组合策略。在一些合适的效用函数下，获得了投资者的最优消费，最优投资组合策略和最优净负债率。我们发现无形资产的价值明确取决于所有市场参数，包括随着时间的推移，投资者的生产率，最优财富和最优债务比率。