scholarly journals STABILITY OF THE EXPONENTIAL UTILITY MAXIMIZATION PROBLEM WITH RESPECT TO PREFERENCES

2014 ◽  
Vol 27 (1) ◽  
pp. 38-67 ◽  
Author(s):  
Hao Xing
Keyword(s):  
Utility Maximization ◽  
Exponential Utility ◽  
Maximization Problem ◽  
Utility Maximization Problem

scholarly journals Life Insurance and Subsistence Consumption with an Exponential Utility

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 358
Author(s):  
Ho-Seok Lee
Keyword(s):  
Mortality Risk ◽  
Life Insurance ◽  
Explicit Solution ◽  
Utility Maximization ◽  
Exponential Utility ◽  
Maximization Problem ◽  
Duality Method ◽  
Utility Maximization Problem

In this paper, we derive an explicit solution to the utility maximization problem of an individual with mortality risk and subsistence consumption constraint. We adopt an exponential utility for the individual’s consumption and the martingale and duality method is employed. From the explicit solution, we exhibit how the mortality intensity and subsistence consumption constraint affect, separately and together, portfolio, consumption and life insurance purchase.

scholarly journals Dual Formulation of the Utility Maximization Problem Under Transaction Costs

2001 ◽  
Vol 11 (4) ◽  
pp. 1353-1383 ◽  
Author(s):  
Griselda Deelstra ◽  
Huyên Pham ◽  
Nizar Touzi
Keyword(s):  
Transaction Costs ◽  
Utility Maximization ◽  
Maximization Problem ◽  
Dual Formulation ◽  
Utility Maximization Problem

scholarly journals Utility Maximization with Proportional Transaction Costs Under Model Uncertainty

2020 ◽  
Vol 45 (4) ◽  
pp. 1210-1236 ◽  
Author(s):  
Shuoqing Deng ◽  
Xiaolu Tan ◽  
Xiang Yu
Keyword(s):  
Dynamic Programming ◽  
Transaction Costs ◽  
Model Uncertainty ◽  
Utility Maximization ◽  
Exponential Utility ◽  
Market Condition ◽  
Maximization Problem ◽  
Proportional Transaction Costs ◽  
Utility Indifference ◽  
Basic Features

We consider a discrete time financial market with proportional transaction costs under model uncertainty and study a numéraire-based semistatic utility maximization problem with an exponential utility preference. The randomization techniques recently developed in Bouchard, Deng, and Tan [Bouchard B, Deng S, Tan X (2019) Super-replication with proportional transaction cost under model uncertainty. Math. Finance 29(3):837–860.], allow us to transform the original problem into a frictionless counterpart on an enlarged space. By suggesting a different dynamic programming argument than in Bartl [Bartl D (2019) Exponential utility maximization under model uncertainty for unbounded endowments. Ann. Appl. Probab. 29(1):577–612.], we are able to prove the existence of the optimal strategy and the convex duality theorem in our context with transaction costs. In the frictionless framework, this alternative dynamic programming argument also allows us to generalize the main results in Bartl [Bartl D (2019) Exponential utility maximization under model uncertainty for unbounded endowments. Ann. Appl. Probab. 29(1):577–612.] to a weaker market condition. Moreover, as an application of the duality representation, some basic features of utility indifference prices are investigated in our robust setting with transaction costs.

scholarly journals SOLVABILITY AND NUMERICAL SIMULATION OF BSDEs RELATED TO BSPDEs WITH APPLICATIONS TO UTILITY MAXIMIZATION

2011 ◽  
Vol 14 (05) ◽  
pp. 635-667 ◽  
Author(s):  
PETER IMKELLER ◽  
ANTHONY RÉVEILLAC ◽  
JIANING ZHANG
Keyword(s):  
Financial Markets ◽  
Existence And Uniqueness ◽  
Utility Maximization ◽  
Optimization Problem ◽  
Terminal Condition ◽  
Quadratic Growth ◽  
Maximization Problem ◽  
Existence Of A Solution ◽  
Utility Maximization Problem ◽  
Portfolio Optimization Problem

In this paper we study BSDEs arising from a special class of backward stochastic partial differential equations (BSPDEs) that is intimately related to utility maximization problems with respect to arbitrary utility functions. After providing existence and uniqueness we discuss the numerical realizability. Then we study utility maximization problems on incomplete financial markets whose dynamics are governed by continuous semimartingales. Adapting standard methods that solve the utility maximization problem using BSDEs, we give solutions for the portfolio optimization problem which involve the delivery of a liability at maturity. We illustrate our study by numerical simulations for selected examples. As a byproduct we prove existence of a solution to a very particular quadratic growth BSDE with unbounded terminal condition. This complements results on this topic obtained in Briand and Hu (2006, 2008) and Briand et al. (2007).

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