scholarly journals State-Dependent Utility

2009 ◽  
Vol 46 (1) ◽  
pp. 55-70 ◽  
Author(s):  
Jaime A. Londoño
Keyword(s):  
General Setting ◽  
Optimal Consumption ◽  
Investment Strategies ◽  
Economic Agents ◽  
State Dependent ◽  
Portfolio Problem ◽  
Functional Forms ◽  
Secondary Result ◽  
The One ◽  
Optimal Consumption And Investment

We propose a new approach to utilities in (state) complete markets that is consistent with state-dependent utilities. Full solutions of the optimal consumption and portfolio problem are obtained in a very general setting which includes several functional forms for utilities used in the current literature, and consider general restrictions on allowable wealths. As a secondary result, we obtain a suitable representation for straightforward numerical computations of the optimal consumption and investment strategies. In our model, utilities reflect the level of consumption satisfaction of flows of cash in future times as they are (uniquely) valued by the market when the economic agents are making their consumption and investment decisions. The theoretical framework used for the model is the one proposed in Londoño (2008). We develop the martingale methodology for the solution of the problem of optimal consumption and investment in this setting.

scholarly journals State-Dependent Utility

2009 ◽  
Vol 46 (01) ◽  
pp. 55-70
Author(s):  
Jaime A. Londoño
Keyword(s):  
General Setting ◽  
Optimal Consumption ◽  
Investment Strategies ◽  
Economic Agents ◽  
State Dependent ◽  
Portfolio Problem ◽  
Functional Forms ◽  
Secondary Result ◽  
The One ◽  
Optimal Consumption And Investment

We propose a new approach to utilities in (state) complete markets that is consistent with state-dependent utilities. Full solutions of the optimal consumption and portfolio problem are obtained in a very general setting which includes several functional forms for utilities used in the current literature, and consider general restrictions on allowable wealths. As a secondary result, we obtain a suitable representation for straightforward numerical computations of the optimal consumption and investment strategies. In our model, utilities reflect the level of consumption satisfaction of flows of cash in future times as they are (uniquely) valued by the market when the economic agents are making their consumption and investment decisions. The theoretical framework used for the model is the one proposed in Londoño (2008). We develop the martingale methodology for the solution of the problem of optimal consumption and investment in this setting.

scholarly journals State-Dependent Utilities and Incomplete Markets

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jaime A. Londoño
Keyword(s):  
Incomplete Markets ◽  
Optimal Consumption ◽  
State Variables ◽  
Main Condition ◽  
Optimization Criteria ◽  
State Dependent ◽  
Arbitrage Opportunities ◽  
Multiple State ◽  
Intertemporal Equilibrium ◽  
Optimal Consumption And Investment

The problem of optimal consumption and investment for an agent that does not influence the market is solved. The optimization criteria are based on a state-dependent utility functional as proposed in Londoño (2009). The proposed solution is given in any market without state-tame arbitrage opportunities, includes several utilities structures, and includesincomplete marketswhere there are multiple state variables. The solutions obtained for optimal wealths consumptions, and portfolios are explicit and easily computable; the main condition for the result to hold is that the income process of each agent is hedgeable, requiring a natural condition on employer and employee to agree on a contract whose risk can be managed by both parties. In this paper we also developed a theory of markets when the processes are generalization of Brownian flows on manifolds, since this framework shows to be the natural one whenever the problem of intertemporal equilibrium is addressed.

Optimal retirement planning under partial information

2019 ◽  
Vol 36 (1-4) ◽  
pp. 37-55
Author(s):  
Nicole Bäuerle ◽  
An Chen
Keyword(s):  
Optimization Problem ◽  
Partial Information ◽  
Comparative Statics ◽  
Optimal Consumption ◽  
Investment Behavior ◽  
Martingale Method ◽  
Investment Strategies ◽  
Relative Risk Aversion ◽  
Closed Form Solutions ◽  
Optimal Consumption And Investment

Abstract The present paper analyzes an optimal consumption and investment problem of a retiree with a constant relative risk aversion (CRRA) who faces parameter uncertainty about the financial market. We solve the optimization problem under partial information by making the market observationally complete and consequently applying the martingale method to obtain closed-form solutions to the optimal consumption and investment strategies. Further, we provide some comparative statics and numerical analyses to deeply understand the consumption and investment behavior under partial information. Bearing partial information has little impact on the optimal consumption level, but it makes retirees with an RRA smaller than one invest more riskily, while it makes retirees with an RRA larger than one invest more conservatively.

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