Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints

Pham,

doi:10.1007/s00245-002-0735-5

Cited by 108 publications

(143 citation statements)

References 14 publications

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“…Since C 2 is arbitrary, we conclude, as in the proof of Theorem 4.1 in Pham (2002), that (A.62) has a smooth solution with polynomial growth condition in y andr.…”

Section: Proof Of Theorem 33supporting

confidence: 61%

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Relative Hedging of Systematic Mortality Risk

Ludkovski

Bayraktar

2009

North American Actuarial Journal

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We study indifference pricing mechanisms for mortality contingent claims under stochastic mortality age structures. Our focus is on capturing the internal cross-hedge between components of an insurer's portfolio, especially between life annuities and life insurance. We carry out an exhaustive analysis of the dynamic exponential premium principle which is the representative nonlinear pricing rule in our framework. Along the way we also derive and compare a variety of linear pricing rules which value claims under various martingale measures. We illustrate our examples with realistic numerical examples that show the relative importance of model parameters.

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“…Since C 2 is arbitrary, we conclude, as in the proof of Theorem 4.1 in Pham (2002), that (A.62) has a smooth solution with polynomial growth condition in y andr.…”

Section: Proof Of Theorem 33supporting

confidence: 61%

“…We will use Theorem 6.6.2 of Fleming and Rishel (1975) and some arguments from the proof of Lemma 4.1 in Pham (2002) to prove our result.…”

Section: Proof Of Theorem 33mentioning

confidence: 99%

Relative Hedging of Systematic Mortality Risk

Ludkovski

Bayraktar

2009

North American Actuarial Journal

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“…From then on, various default-free optimal investment models have been proposed and investigated in the literature (see, e.g. [6], [11], [17], [22], and [23]). Among them, Fleming and Pang [11] discussed a classical Merton portfolio optimization problem, where the interest rate is assumed to fluctuate from time to time.…”

Section: Introductionmentioning

confidence: 99%

“…In a subsequent paper, Pang [22] treated the analogue problem with log utility. Pham [23] studied an optimal investment problem, in which the instantaneous rate and the volatility are assumed to rely on a stochastic factor that is described by a Markov diffusion process, and the goal is to maximize the expected HARA utility of the terminal wealth.…”

Section: Introductionmentioning

confidence: 99%

“…(This assumption seems to be reasonable, and has been adopted in some known references; see, e.g. [23]. In fact, the stochastic differential equations in which the characteristic parameters depend on economic factors (state variables) are often used in finance to model different types of economic phenomenon, such as the random fluctuant interest rate and stochastic volatility; see, e.g.…”

Section: Introductionmentioning

confidence: 99%

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An optimal portfolio problem in a defaultable market

Wang

Yang

2010

Adv. Appl. Probab.

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We consider a portfolio optimization problem in a defaultable market. The investor can dynamically choose a consumption rate and allocate his/her wealth among three financial securities: a defaultable perpetual bond, a default-free risky asset, and a money market account. Both the default risk premium and the default intensity of the defaultable bond are assumed to rely on some stochastic factor which is described by a diffusion process. The goal is to maximize the infinite-horizon expected discounted log utility of consumption. We apply the dynamic programming principle to deduce a HamiltonJacobi-Bellman equation. Then an optimal Markov control policy and the optimal value function is explicitly presented in a verification theorem. Finally, a numerical analysis is presented for illustration.

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Investment and Valuation Under Backward and Forward Dynamic Exponential Utilities in a Stochastic Factor Model

Musiela

Zariphopoulou

Applied and Numerical Harmonic Analysis

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Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints

Cited by 108 publications

References 14 publications

Relative Hedging of Systematic Mortality Risk

Relative Hedging of Systematic Mortality Risk

An optimal portfolio problem in a defaultable market

Investment and Valuation Under Backward and Forward Dynamic Exponential Utilities in a Stochastic Factor Model

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