Indifference pricing and hedging in a multiple-priors model with trading constraints

Huang, Yan; Liang, Gechun; Yang, Zhou

doi:10.1007/s11425-014-4885-0

Cited by 10 publications

(17 citation statements)

References 25 publications

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“…Then v satisfies the following VI (see Next, we prove v ≥ v in Ω y T −δ . In fact, the comparison principle for VI (see [22]) implies that it is sufficient to show that Hence, we conclude that L − Ke y is indeed a subsolution of (3.25).…”

Section: Theorem 32 (Position Of the Free Boundary)mentioning

confidence: 70%

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Dynkin game of convertible bonds and their optimal strategy

Huang

Yang

et al. 2015

Journal of Mathematical Analysis and Applications

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This paper studies the valuation and optimal strategy of convertible bonds as a Dynkin game by using the reflected backward stochastic differential equation method and the variational inequality method. We first reduce such a Dynkin game to an optimal stopping time problem with state constraint, and then in a Markovian setting, we investigate the optimal strategy by analyzing the properties of the corresponding free boundary, including its position, asymptotics, monotonicity and regularity. We identify situations when call precedes conversion, and vice versa. Moreover, we show that the irregular payoff results in the possibly non-monotonic conversion boundary. Surprisingly, the price of the convertible bond is not necessarily monotonic in time: it may even increase when time approaches maturity.

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Section: Theorem 32 (Position Of the Free Boundary)mentioning

confidence: 70%

“…Next, we prove that v is the unique W 2 p, loc (Ω) ∩ C( Ω ) ∩ L ∞ (Ω) solution of the VI (3.16). In fact, the uniqueness follows from the comparison principle for VI (see [22]), and it is easy to verify the regularity of the solution. Then it is sufficient to prove that v satisfies the VI (3.16).…”

Section: Theorem 32 (Position Of the Free Boundary)mentioning

confidence: 99%

Dynkin game of convertible bonds and their optimal strategy

Huang

Yang

et al. 2015

Journal of Mathematical Analysis and Applications

Self Cite

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“…By the comparison principle for VIs (see, e.g., Friedman (1982), Yan et al (2015)), we have V (t, x) ≥ V (t, x) for t ∈ [t 1 , T ], while it is clear that V (t, x) ≤ V (t, x). Therefore, V (t, x) = V (t, x) for t ∈ [t 1 , T ].…”

Section: A3 Proof Of Lemmamentioning

confidence: 99%

Optimal Expansion of Business Opportunity

Chen¹,

Chiu²,

Wong³

2021

Preprint

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Any firm whose business strategy has an exposure constraint that limits its potential gain naturally considers expansion, as this can increase its exposure. We model business expansion as an enlargement of the opportunity set for business policies. However, expansion is irreversible and has an opportunity cost attached. We use the expected optimization of utility to formulate this as a novel stochastic control problem combined with an optimal stopping time, and we derive an explicit solution for exponential utility.We apply the framework to an investment and a reinsurance scenario. In the investment problem, the cost and incentives to increase the trading exposure are analyzed, while the optimal timing for an insurer to launch its reinsurance business is investigated in the reinsurance problem. Our model predicts that the additional income gained through business expansion is the key incentive for a decision to expand. Interestingly, companies may have this incentive but are likely to wait for a period of time before expanding, although situations of zero opportunity cost or specific restrictive conditions on the model parameters are exceptions to waiting. The business policy remains on the boundary of the opportunity set before expansion during the waiting period. The length of the waiting period is related to the opportunity cost, return, and risk of the expanded business.

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“…The current paper is committed to studying recursive utility optimization under closed constraints. This kind of constraint also appeared in Yan, Liang and Yang (2015), but they considered utility indifference valuation problem, where the utility is formulated as a stochastic differential utility (SDU).…”

Section: Introductionmentioning

confidence: 99%

Optimal consumption and portfolio selection with Epstein-Zin utility under general constraints

Feng¹,

Tian²

2021

Preprint

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In this paper, we investigate the consumption-investment problem for an investor with Epstein-Zin utility under general constraints. In an incomplete market, we impose closed, not necessarily convex, constraints on strategies and characterize optimal consumption and investment strategies via backward stochastic differential equations (BSDEs). Due to the stochastic environment of the market, the solution to this BSDE is unbounded and thereby the BMO argument breaks down. We use the Lyapunov function to show a certain local martingale is a martingale and complete our proof by the martingale optimal principle. Finally, an explicit model is given to illustrate the main result.

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Indifference pricing and hedging in a multiple-priors model with trading constraints

Cited by 10 publications

References 25 publications

Dynkin game of convertible bonds and their optimal strategy

Dynkin game of convertible bonds and their optimal strategy

Optimal Expansion of Business Opportunity

Optimal consumption and portfolio selection with Epstein-Zin utility under general constraints

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