Utility Indifference Pricing and Other Topics

2019 ◽  
pp. 436-440
Author(s):  
Tomas Björk
Keyword(s):  
Incomplete Markets ◽  
Utility Functions ◽  
Equilibrium Theory ◽  
Local Version ◽  
Indifference Pricing ◽  
Discount Factors ◽  
Utility Indifference Pricing ◽  
Stochastic Discount Factors ◽  
Utility Indifference

In this chapter we discuss two methods of pricing in incomplete markets, based on utility functions. This theory comes in the shape of a global and a local version. Both versions are discussed, and for the local version we connect to the theory of stochastic discount factors and equilibrium theory.

A NOTE ON UTILITY INDIFFERENCE PRICING

2016 ◽  
Vol 19 (06) ◽  
pp. 1650037
Author(s):  
JOHANNES GERER ◽  
GREGOR DORFLEITNER
Keyword(s):  
Utility Functions ◽  
Indifference Pricing ◽  
Market Incompleteness ◽  
Utility Indifference Pricing ◽  
Marginal Prices ◽  
Utility Indifference ◽  
Contingent Claim Pricing ◽  
The Many ◽  
Many Sources ◽  
Continuous Trading

Utility-based valuation methods are enjoying growing popularity among researchers as a means to overcome the challenges in contingent claim pricing posed by the many sources of market incompleteness. However, we show that under the most common utility functions (including CARA and CRRA), any realistic and actually practicable hedging strategy involving a possible short position has infinitely negative utility. We then demonstrate for utility indifference prices (and also for the related so-called utility-based (marginal) prices) how this problem leads to a severe divergence between results obtained under the assumption of continuous trading and realistic results. The combination of continuous trading and common utility functions is thus not justified in these methods, raising the question of whether and how results obtained under such assumptions could be put to real-world use.

Company stock rewards on the evaluation of investor’s remuneration package with stochastic income

2019 ◽  
Vol 06 (02) ◽  
pp. 1950017
Author(s):  
Kebareng I. Moalosi-Court ◽  
Edward M. Lungu ◽  
Elias R. Offen
Keyword(s):  
Value Function ◽  
Optimal Investment ◽  
Stock Option ◽  
Utility Functions ◽  
Risk Averse ◽  
Indifference Pricing ◽  
Company Stock ◽  
Utility Indifference Pricing ◽  
Utility Indifference ◽  
Total Wealth

We consider a risk averse investor as are who has a bond, is rewarded with [Formula: see text] units of company stock option and is endowed with stochastic income. First, we derive and analyzes the optimal investment threshold and investment value function of the investor. Second, we determine a remuneration package and the utility indifference pricing of this risk averse investor and analyze the results for two utility functions; the exponential and logarithmic utilities. From these results, we conclude that the more units of company stock the investor receives, the higher the chances of increasing the total wealth or profit.

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