A Note on Irreversible Investment, Hedging and Optimal Consumption Problems

Henderson, Vicky; Hobson, David

doi:10.1142/s021902490600386x

Int. J. Theor. Appl. Finan.

2006

DOI: 10.1142/s021902490600386x

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A Note on Irreversible Investment, Hedging and Optimal Consumption Problems

Vicky Henderson

David Hobson

Abstract: A canonical problem in real option pricing, as described in the classic text of Dixit and Pindyck [2], is to determine the optimal time to invest at a fixed cost, to receive in return a stochastic cashflow. In this paper we are interested in this problem in an incomplete market where the cashflow is not spanned by the traded assets. We follow the formulation in Miao and Wang [21]; our contribution is to show that significant progress can be made in solving the Hamilton-Jacobi-Bellman equation and that the opti… Show more

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Cited by 3 publications

References 22 publications

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Perpetual American options in incomplete markets: the infinitely divisible case

Henderson

Hobson

2008

Quantitative Finance

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We consider the exercise of a number of American options in an incomplete market. In this paper we are interested in the case where the options are infinitely divisible. We make the simplifying assumptions that the options have infinite maturity, and the holder has exponential utility. Our contribution is to solve this problem explicitly and we show that, except at the initial time when it may be advantageous to exercise a positive fraction of his holdings, it is never optimal for the holder to exercise a tranche of options. Instead, the process of option exercises is continuous; however, it is singular with respect to calendar time. Exercise takes place when the stock price reaches a convex boundary which we identify.Perpetual American options, Incomplete markets, Infinitely divisible,

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Perpetual American options in incomplete markets: the infinitely divisible case

Henderson

Hobson

2008

Quantitative Finance

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Real Options Games in Complete and Incomplete Markets with Several Decision Makers

Bensoussan¹,

Diltz²,

Hoe³

2010

SIAM J. Finan. Math.

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Abstract. We consider optimal investment policies for irreversible capital investment projects under uncertainty in a monopoly situation and in a Stackelberg leader-follower game. We consider two types of payoffs: lump-sum and cash flows. The decisions are the times to enter into the market. The problems belong to the class of optimal stopping times, for which the right approach is that of variational inequalities (V.I.s). In the case of complete markets, payoffs are expected values with respect to the risk-neutral probability. In the case of incomplete markets, the risk-neutral probability is not defined. We consider an investor maximizing his/her utility function, and we consider the investment in the project as an additional decision, besides portfolio investment and consumption decisions. This decision remains a stopping time, conversely to the portfolio investment and consumption decisions (continuous controls). The game problem raises new difficulties. The leader's V.I. has a nondifferentiable obstacle. The weak formulation of the V.I. handles this difficulty. In some cases, the solution of the V.I. may be continuously differentiable although the obstacle is not. An additional difficulty occurs for lump-sum payoffs in the case of incomplete markets. We cannot compare gains and losses at different times. We propose an alternative approach, using equivalence (indifference) considerations. In the case of payoffs characterized by cash flows, this difficulty does not exist, but an intermediary problem arises which has a nice interpretation as a differential game. The solutions thus obtained for the Stackelberg game are not intuitive. Therefore, competition has important consequences on investment decisions.

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Investment Timing Under Regime Switching

Elliott

Miao

2009

Int. J. Theor. Appl. Finan.

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We investigate the optimal investment timing strategy in a real option framework. Depending on the state of the economy, whose changes are modeled by a Markov chain, the investment cost can take one of two values. The optimal investment timing decision is determined by finding the free boundary of a perpetual American option. Three investment timing policies, based on different assumptions of investors' information sets, are determined and compared. In the full information case, a significantly earlier optimal exercising time is indicated. We show that an optimal-timing policy suggested by the conventional real option model might ruin the investment opportunities.

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A Note on Irreversible Investment, Hedging and Optimal Consumption Problems

Cited by 3 publications

References 22 publications

Perpetual American options in incomplete markets: the infinitely divisible case

Perpetual American options in incomplete markets: the infinitely divisible case

Real Options Games in Complete and Incomplete Markets with Several Decision Makers

Investment Timing Under Regime Switching

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