Abstract
This paper discusses optimal portfolio with discounted stochastic cash inflows (SCI). The cash inflows are invested into a market that is characterized by a stock and a cash account. It is assumed that the stock and the cash inflows are stochastic and the stock is modeled by a semi-martingale. The Inflation linked bond and the cash inflows are Geometric. The cash account is deterministic. We do some scientific analyses to see how the discounted stochastic cash inflow is affected by some of the parameters. Under this setting, we develop an optimal portfolio formula and later give some numerical results.
Highlights
For example in financial mathematics, the classical model for a stock price is that of a geometric Brownian motion
We develop an optimal portfolio formula and later give some numerical results
We show that when t = 0, the portfolio value is −0.057 which is equivalent to −5.7% when the value of the wealth is 40,000 and the portfolio value is −0.0613 which is equivalent to −6.13% when the value of the wealth is 1,000,000
Summary
For example in financial mathematics, the classical model for a stock price is that of a geometric Brownian motion. Liu et al (2003) [3] solved for the optimal portfolio in a model with stochastic volatility and jumps when the investor can trade the stock and a risk-free asset only They found that Liu and Pan (2003) [4] extended this paper to the case of a complete market. In Guo and Xu (2004) [7], researchers applied the mean-variance analysis approach to model the portfolio selection problem They considered a financial market containing d + 1 assets: d risky stocks and one bond. A sufficient maximum principle for the optimal control of jump diffusions is used showing dynamic programming and going applications to financial optimization problem in a market described by such process. Most calculations and methods used were influenced by the works of Nkeki [1], Nkeki [13] ∅ksendal [14], ∅ksendal and Sulem [12], Klebaner [15] and Cont and Tankov [16]
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