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The Capitalist Spirit: Optimal Consumption and Investment When Wealth Enters Utility Directly

  • Joonglee Jo Graduate Department of Financial Engineering, Ajou University, Graduate Department of Financial Engineering, Ajou University
  • Hyeng Keun Koo Graduate Department of Financial Engineering, Ajou University, Suwon 443-749, Korea
  • Shanjian Tang School of Mathematical Science, Fudan University, Shanghai 200433, China, Graduate Department of Financial Engineering, Ajou University
This paper studies a continuous-time model of consumption and investment with a utility function where wealth enters as an argument. The stochastic maximum principle is used to obtain a solution and compared with a newly formulated mar- tingale method. A concrete solution is obtained by a discrete time approximation. An agent with such a utility function typically exhibits decreasing marginal propen- sity to consume and an increasing marginal propensity to invest in the risky assets consistent with empirical evidence.

  • Joonglee Jo
  • Hyeng Keun Koo
  • Shanjian Tang
This paper studies a continuous-time model of consumption and investment with a utility function where wealth enters as an argument. The stochastic maximum principle is used to obtain a solution and compared with a newly formulated mar- tingale method. A concrete solution is obtained by a discrete time approximation. An agent with such a utility function typically exhibits decreasing marginal propen- sity to consume and an increasing marginal propensity to invest in the risky assets consistent with empirical evidence.