Existence and uniqueness of optimal consumption and portfolio rules in a continuous-time finance model with habit formation and without short sales

1997 ◽  
Vol 28 (2) ◽  
pp. 187-205 ◽  
Author(s):  
Xing Jin ◽  
Shuhui Deng
Keyword(s):  
Continuous Time ◽  
Existence And Uniqueness ◽  
Habit Formation ◽  
Optimal Consumption ◽  
Short Sales ◽  
Finance Model ◽  
Continuous Time Finance

Optimal Consumption and Insurance: A Continuous-time Markov Chain Approach

2008 ◽  
Vol 38 (01) ◽  
pp. 231-257 ◽  
Author(s):  
Holger Kraft ◽  
Mogens Steffensen
Keyword(s):  
Continuous Time ◽  
Optimal Solution ◽  
Decision Problems ◽  
Optimal Consumption ◽  
Continuous Time Markov Chain ◽  
Financial Decision Making ◽  
Markov Chain Approach ◽  
Special Cases ◽  
Financial Decision ◽  
The Individual

Personal financial decision making plays an important role in modern finance. Decision problems about consumption and insurance are in this article modelled in a continuous-time multi-state Markovian framework. The optimal solution is derived and studied. The model, the problem, and its solution are exemplified by two special cases: In one model the individual takes optimal positions against the risk of dying; in another model the individual takes optimal positions against the risk of losing income as a consequence of disability or unemployment.

scholarly journals Optimal consumption of multiple goods in incomplete markets

2018 ◽  
Vol 55 (3) ◽  
pp. 810-822
Author(s):  
Oleksii Mostovyi
Keyword(s):  
Closed Form ◽  
Incomplete Markets ◽  
Existence And Uniqueness ◽  
Dual Problem ◽  
Optimal Consumption ◽  
Closed Form Solutions ◽  
Uniqueness Of The Solution ◽  
Incomplete Models

Abstract We consider the problem of optimal consumption of multiple goods in incomplete semimartingale markets. We formulate the dual problem and identify conditions that allow for the existence and uniqueness of the solution, and provide a characterization of the optimal consumption strategy in terms of the dual optimizer. We illustrate our results with examples in both complete and incomplete models. In particular, we construct closed-form solutions in some incomplete models.

Continuous-Time Finance.

1991 ◽  
Vol 46 (4) ◽  
pp. 1567
Author(s):  
Stephen A. Ross ◽  
Robert C. Merton
Keyword(s):  
Continuous Time ◽  
Continuous Time Finance

Effect of the Return Policy in a Continuous-Time Newsvendor Problem

2017 ◽  
Vol 34 (06) ◽  
pp. 1750031
Author(s):  
Weiwei Zhang ◽  
Zhongfei Li ◽  
Ke Fu ◽  
Fan Wang
Keyword(s):  
Diffusion Process ◽  
Continuous Time ◽  
Existence And Uniqueness ◽  
Stackelberg Game ◽  
Jump Diffusion ◽  
Newsvendor Problem ◽  
Stackelberg Equilibrium ◽  
Computational Results ◽  
Return Policy ◽  
Demand Rate

This paper studies the stochastic differential Stackelberg game in a continuous-time newsvendor problem with a return policy, in which one supplier sells products to one retailer and the two parties make the decisions sequentially to maximize their own expected profits. When the demand process is a general jump-diffusion process, we provide a general formula for the equilibrium if it exists. When the demand rate is an Ornstein–Uhlenbeck (O–U) process, we prove the existence and uniqueness of the equilibrium and find an explicit expression for the equilibrium. Computational results show that the return policy has significant impact on the Stackelberg equilibrium.

Continuous-Time Finance.

1991 ◽  
Vol 101 (406) ◽  
pp. 643
Author(s):  
Michael J. P. Selby ◽  
Robert C. Merton
Keyword(s):  
Continuous Time ◽  
Continuous Time Finance
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