scholarly journals Optimal investment and consumption with labor income in incomplete markets

2020 ◽  
Vol 30 (2) ◽  
pp. 747-787
Author(s):  
Oleksii Mostovyi ◽  
Mihai Sîrbu
Keyword(s):  
Incomplete Markets ◽  
Optimal Investment ◽  
Labor Income ◽  
Optimal Investment And Consumption

scholarly journals Optimal Investment-Consumption Strategy under Inflation in a Markovian Regime-Switching Market

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Huiling Wu
Keyword(s):  
Regime Switching ◽  
Stock Price ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Power Utility ◽  
Optimal Investment Strategy ◽  
Admissible Strategies ◽  
Definition Of ◽  
Markovian Regime Switching ◽  
Optimal Investment And Consumption

This paper studies an investment-consumption problem under inflation. The consumption price level, the prices of the available assets, and the coefficient of the power utility are assumed to be sensitive to the states of underlying economy modulated by a continuous-time Markovian chain. The definition of admissible strategies and the verification theory corresponding to this stochastic control problem are presented. The analytical expression of the optimal investment strategy is derived. The existence, boundedness, and feasibility of the optimal consumption are proven. Finally, we analyze in detail by mathematical and numerical analysis how the risk aversion, the correlation coefficient between the inflation and the stock price, the inflation parameters, and the coefficient of utility affect the optimal investment and consumption strategy.

scholarly journals On Market Completions Approach to Option Pricing

2021 ◽  
Vol 9 (3) ◽  
pp. 77-93
Author(s):  
I. Vasilev ◽  
A. Melnikov
Keyword(s):  
Option Pricing ◽  
Incomplete Markets ◽  
Option Price ◽  
Optimal Investment ◽  
Market Model ◽  
Option Prices ◽  
End Points ◽  
Hedging Strategies ◽  
Risk Neutral ◽  
Interesting Approach

Option pricing is one of the most important problems of contemporary quantitative finance. It can be solved in complete markets with non-arbitrage option price being uniquely determined via averaging with respect to a unique risk-neutral measure. In incomplete markets, an adequate option pricing is achieved by determining an interval of non-arbitrage option prices as a region of negotiation between seller and buyer of the option. End points of this interval characterise the minimum and maximum average of discounted pay-off function over the set of equivalent risk-neutral measures. By estimating these end points, one constructs super hedging strategies providing a risk-management in such contracts. The current paper analyses an interesting approach to this pricing problem, which consists of introducing the necessary amount of auxiliary assets such that the market becomes complete with option price uniquely determined. One can estimate the interval of non-arbitrage prices by taking minimal and maximal price values from various numbers calculated with the help of different completions. It is a dual characterisation of option prices in incomplete markets, and it is described here in detail for the multivariate diffusion market model. Besides that, the paper discusses how this method can be exploited in optimal investment and partial hedging problems.

scholarly journals Optimal Investment and Consumption for Multidimensional Spread Financial Markets with Logarithmic Utility

Stats ◽  
2021 ◽  
Vol 4 (4) ◽  
pp. 1012-1026
Author(s):  
Sahar Albosaily ◽  
Serguei Pergamenchtchikov
Keyword(s):  
Financial Markets ◽  
Numerical Simulations ◽  
Financial Market ◽  
Optimal Investment ◽  
Optimal Consumption ◽  
Dynamical Programming ◽  
Verification Theorem ◽  
Logarithmic Utility ◽  
Hamilton Jacobi Bellman ◽  
Optimal Investment And Consumption

We consider a spread financial market defined by the multidimensional Ornstein–Uhlenbeck (OU) process. We study the optimal consumption/investment problem for logarithmic utility functions using a stochastic dynamical programming method. We show a special verification theorem for this case. We find the solution to the Hamilton–Jacobi–Bellman (HJB) equation in explicit form and as a consequence we construct optimal financial strategies. Moreover, we study the constructed strategies with numerical simulations.

Portfolio Optimization in Incomplete Markets

2019 ◽  
pp. 426-435
Author(s):  
Tomas Björk
Keyword(s):  
Portfolio Optimization ◽  
Incomplete Markets ◽  
Duality Theory ◽  
Optimal Investment ◽  
Optimal Consumption ◽  
Finite Sample ◽  
Martingale Approach ◽  
Dual Approach ◽  
Full Theory ◽  
Optimal Investment Problem

The object of this chapter is to give an overview of the dual approach to portfolio optimization in incomplete markets. The main result of this theory is that to every optimal investment problem there is a dual problem where we minimize a dual objective function over the class of martingale measures. For the case of a finite sample space we can present the full theory, but for the general case we only outline the proof. The theory is closely connected to convex duality theory and to the martingale approach to optimal consumption/investment discussed in Chapter 27.

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