Optimal Investment in Incomplete Markets

2018 ◽  
pp. 327-341
Author(s):  
Jia-An Yan
Keyword(s):  
Incomplete Markets ◽  
Optimal Investment

scholarly journals Optimal investment in incomplete markets when wealth may become negative

2001 ◽  
Vol 11 (3) ◽  
pp. 694-734 ◽  
Author(s):  
Walter Schachermayer
Keyword(s):  
Incomplete Markets ◽  
Optimal Investment

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.

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.

scholarly journals Optimal investment with random endowments in incomplete markets

2004 ◽  
Vol 14 (2) ◽  
pp. 845-864 ◽  
Author(s):  
Julien Hugonnier ◽  
Dmitry Kramkov
Keyword(s):  
Incomplete Markets ◽  
Optimal Investment

scholarly journals An Optimal Investment Strategy for Insurers in Incomplete Markets

Risks ◽  
2018 ◽  
Vol 6 (2) ◽  
pp. 31
Author(s):  
Mohamed Badaoui ◽  
Begoña Fernández ◽  
Anatoliy Swishchuk
Keyword(s):  
Incomplete Markets ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Optimal Investment Strategy
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