Suchergebnisse

AbstractThe problem of choosing an optimal replacement rule is considered for deteriorating equipment where the amount of deterioration is observed periodically. A "near" optimal rule is obtained. The main tool is an optimal stopping lemma related to semimartingales.

AbstractLeasing valuation is a topic that has aroused considerable interest in business circles. This paper examines leasing from the point of view of the lessor who can decide to leave the contract due to default. We analyze in introducing a model in which the lessor decides whether or not to terminate the contract at a given point in time, comparing it with the cost of capital of alternative investments. The proposed model is stochastic, and it is strongly based on correlated random walks, making it more adaptable to real-world circumstances. Furthermore, we propose a recombinant binomial tree based on correlated random walks, performing numerical simulations starting from CIR and Vasicek models. We will point out that as the rate of cost of capital of an alternative investment increases, the optimal boundary curve decreases, so the lessor leaves, while as the past interest rates increases, the curve rises and the lessor will have a concrete interest in maintaining the contract.

We consider a government that aims at reducing the debt-to-gross domestic product (GDP) ratio of a country. The government observes the level of the debt-to-GDP ratio and an indicator of the state of the economy, but does not directly observe the development of the underlying macroeconomic conditions. The government's criterion is to minimize the sum of the total expected costs of holding debt and of debt's reduction policies. We model this problem as a singular stochastic control problem under partial observation. The contribution of the paper is twofold. Firstly, we provide a general formulation of the model in which the level of debt-to-GDP ratio and the value of the macroeconomic indicator evolve as a diffusion and a jump-diffusion, respectively, with coefficients depending on the regimes of the economy. These are described through a finite-state continuous-time Markov chain. We reduce via filtering techniques the original problem to an equivalent one with full information (the so-called separated problem), and we provide a general verification result in terms of a related optimal stopping problem under full information. Secondly, we specialize to a case study in which the economy faces only two regimes, and the macroeconomic indicator has a suitable diffusive dynamics. In this setting we provide the optimal debt reduction policy. This is given in terms of the continuous free boundary arising in an auxiliary fully two-dimensional optimal stopping problem.

Most of the investments in practice are carried out without certain horizons. There are many factors to drive investment to a stop. In this paper, we consider a portfolio selection policy with market-related stopping time. Particularly, we assume that the investor exits the market once his wealth reaches a given investment target or falls below a bankruptcy threshold. Our objective is to minimize the expected time when the investment target is obtained, at the same time, we guarantee the probability that bankruptcy happens is no larger than a given level. We formulate the problem as a mix integer linear programming model and make analysis of the model by using a numerical example.

We deal with the pricing of callable Russian options. A callable Russian option
is a contract in which both of the seller and the buyer have the rights to cancel and to exercise at any time,
respectively. The pricing of such an option can be formulated as an optimal stopping problem between the
seller and the buyer, and is analyzed as Dynkin game. We derive the value function of callable Russian
options and their optimal boundaries.

Here, two highly experienced authors present an alternative approach to optimal stopping problems. The basic ideas and techniques of the approach can be explained much simpler than the standard methods in the literature on optimal stopping problems. The monograph will teach the reader to apply the technique to many problems in economics and finance, including new ones. From the technical point of view, the method can be characterized as option pricing via the Wiener-Hopf factorization.