• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.1
• /
• pp.145-149
• /
• 2014

I consider the optimal consumption and portfolio selection problem with nonnegative wealth constraints using the dynamic programming approach. I use the constant relative risk aversion (CRRA) utility function and disutility to derive the closed-form solutions.

• East Asian mathematical journal
• /
• v.36 no.1
• /
• pp.91-99
• /
• 2020

This paper obtains an explicit expression for a debtor's consumption, porfolio and time for filing for bankruptcy when the debtor is subject to upper bound on consumption rate. The utility of consumption is CRRA type and the dynamic programming principle is applied.

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.2
• /
• pp.277-281
• /
• 2012

I study an optimal consumption and portfolio selection problem with regime-switching using a dynamic programming method. With constant relative risk aversion (CRRA) utility I obtain optimal solutions in closed-form.

• Management Science and Financial Engineering
• /
• v.22 no.1
• /
• pp.13-20
• /
• 2016

We investigate the optimal consumption and investment problem when a working debtor has an option to file for bankruptcy. By applying the duality approach, the closed-form solutions are obtained for the case of CRRA utility function. The optimal bankruptcy time is determined by the first hitting time when the financial wealth hits the wealth threshold derived from the optimal stopping time problem. Moreover, the numerical results show that the investment increases as the wealth approaches the threshold and the value gain from the bankruptcy option is vanished as wealth increases.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.2
• /
• pp.329-336
• /
• 2016

The optimal portfolio choice problem with a stochastic income is considered in continuous-time framework. We provide a novel approach to treat the stochastic income when the market is complete. The developed method is useful to obtain closed-form solutions of the problems under borrowing constraints.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.2
• /
• pp.343-349
• /
• 2013

The optimal portfolio selection problem under inflation risk is considered in this paper. There are three assets the economic agent can invest, which are a risk free bond, an index bond and a risky asset. By applying the martingale method, the optimal consumption rate and the optimal portfolios for each asset are obtained explicitly.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.2
• /
• pp.375-383
• /
• 2016

This paper investigates an optimal consumption, portfolio, and life insurance strategies of a family when there is a borrowing constraint and risk aversion change at the time of death of the breadwinner. A CRRA utility is employed and by using the dynamic programming method, we obtain analytic expressions for the optimal strategies.

• Korean Management Science Review
• /
• v.30 no.1
• /
• pp.167-181
• /
• 2013

We investigate the dynamic asset allocation problem under inflation risk when the wealth of an investor is constrained with minimum requirements. To capture the investor's risk preference, the CRRA utility function is considered and he maximizes his expected utility at predetermined date of the refund by participation in the financial market. The financial market is supposed to consist of three kinds of financial instruments which are a risk free asset, a risky asset, and an index bond. The role of an index bond is managing inflation risk represented by price process. The optimal wealth and the optimal asset allocation are derived explicitly by using the method to get the European call option pricing formula. From the numerical results, it is confirmed that the investments on index bond is high when the investor's wealth level is low. However, as his wealth increases, the investments on index bond decreases and he invests on risky asset more. Furthermore, the minimum wealth constraint induces lower investment on risky asset but the effect of the constraints is reduced as the wealth level increases.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.18 no.4
• /
• pp.283-294
• /
• 2014

In this paper we study consumption-labor supply decision of an agent who prepares for retirement at a known time in the future. The agent is assumed to have a preference which is represented by the von Neumann-Morgenstern utility function in which the felicity function has constant relative risk aversion over the composite of consumption and leisure. The composite is obtained by the Cobb-Douglas function. A general problem has been studied by Bodie et al. (2004). We contribute to the literature by deriving the Slutsky equations and conducting comparative statics. In particular, we show that wealth effect can exhibit an interesting property depending upon the time until retirement, as the interest rate increases.