scholarly journals Limiting Distribution of the Present Value of a Portfolio

1994 ◽  
Vol 24 (1) ◽  
pp. 47-60 ◽  
Author(s):  
Gary Parker
Keyword(s):  
Interest Rates ◽  
Limiting Distribution ◽  
Present Value ◽  
Uhlenbeck Process ◽  
Insurance Contracts ◽  
Ornstein Uhlenbeck Process ◽  
Force Of Interest ◽  
The One

AbstractAn approximation of the distribution of the present value of the benefits of a portfolio of temporary insurance contracts is suggested for the case where the size of the portfolio tends to infinity. The model used is the one presented in Parker (1922b) and involves random interest rates and future lifetimes. Some justifications of the approximation are given. Illustrations for limiting portfolios of temporary insurance contracts are presented for an assumed Ornstein-Uhlenbeck process for the force of interest.

scholarly journals A portfolio of endowment policies and its limiting distribution

1996 ◽  
Vol 26 (1) ◽  
pp. 25-33 ◽  
Author(s):  
Gary Parker
Keyword(s):  
Interest Rates ◽  
Limiting Distribution ◽  
Endowment Insurance ◽  
Present Value ◽  
Insurance Contracts ◽  
The One ◽  
The Relationship

AbstractTwo methods for approximating the limiting distribution of the present value of the benefits of a portfolio of identical endowment insurance contracts are suggested. The model used assumes that both future lifetimes and interest rates are random. The first method is similar to the one presented in Parker (1994b). The second method is based on the relationship between temporary and endowment insurance contracts.

On American Derivatives and Related Obstacle Problems

2003 ◽  
Vol 06 (06) ◽  
pp. 565-591 ◽  
Author(s):  
Jörg Kampen
Keyword(s):  
Interest Rates ◽  
Stochastic Volatility ◽  
Obstacle Problems ◽  
Stochastic Volatility Models ◽  
Uhlenbeck Process ◽  
Typical Situation ◽  
Motion Models ◽  
Volatility Models ◽  
Ornstein Uhlenbeck Process ◽  
Classical Models

We derive obstacle problems for pricing of American derivatives with multiple underlyings heuristically using only a few postulates such that classical (Brownian motion) models as well as models based on Levy processes can be considered in our frame. For the classical models we define a "signed measure" which allows to compute the exercise region near maturity and obtain a generic condition for continuity of the free boundary and prove some more general features of exercise regions for classical models. Especially, we investigate the exercise regions of the most important American derivatives with one and multiple underlyings where we include dependence of volatility and interest rates on time and the underlyings extending and recovering some classical results. Further applications include stochastic volatility models. It is shown that in classical stochastic volatility models where volatility is driven by an Ornstein-Uhlenbeck process an American compound call has a nonempty exercise region and compute the exercise region near expiration in a typical situation.

Markov Branching Decision Chains with Interest-Rate-Dependent Rewards

1995 ◽  
Vol 9 (1) ◽  
pp. 99-121 ◽  
Author(s):  
Ying Huang ◽  
Arthur F. Veinott
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Optimal Policy ◽  
Linear Program ◽  
Present Value ◽  
Constraint Matrix ◽  
Rate Dependent ◽  
Markov Decision ◽  
The Interest Rate ◽  
The One

Finite-state-and-action Markov branching decision chains are studied with bounded endogenous expected population sizes and interest-rate-dependent one-period rewards that are analytic in the interest rate at zero. The existence of a stationary strong-maximum-present-value policy is established. Miller and Veinott's [1969] strong policy-improvement method is generalized to find in finite time a stationary n-present-value optimal policy and, when the one-period rewards are rational in the interest rate, a stationary strong-maximum-present-value policy. This extends previous studies of Blackwell [1962], Miller and Veinott [1969], Veinott [1974], and Rothblum [1974, 1975], in which the one-period rewards are independent of the interest rate, and Denardo [1971] in which semi-Markov decision chains with small interest rates are studied. The problem of finding a stationary n-present-value optimal policy is also formulated as a staircase linear program in which the objective function and right-hand sides, but not the constraint matrix, depend on the interest rate, and solutions for all small enough positive interest rates are sought. The optimal solutions of the primal and dual are polynomials in the reciprocal of the interest rate. A constructive rule is given for finding a stationary n-present-value optimal policy from an optimal solution of the asymptotic linear program. This generalizes the linear programming approaches for finding maximum-reward-rate and maximum-present-value policies for Markov decision chains studied by Manne [1960], d'Epenoux [1960, 1963], Balinski [1961], Derman [1962], Denardo and Fox [1968], Denardo [1970], Derman and Veinott [1972], Veinott [1973], and Hordijk and Kallenberg [1979, 1984].

scholarly journals Hidden Geometry of Bidirectional Grid-Constrained Stochastic Processes

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Aldo Taranto ◽  
Shahjahan Khan
Keyword(s):  
Interest Rates ◽  
Stochastic Processes ◽  
Chemical Reactions ◽  
Parabolic Cylinder ◽  
Concentration Gradients ◽  
Uhlenbeck Process ◽  
Geometric Properties ◽  
Extensive Simulation ◽  
Ornstein Uhlenbeck Process

Bidirectional Grid Constrained (BGC) stochastic processes (BGCSPs) are constrained Itô diffusions with the property that the further they drift away from the origin, the more the resistance to movement in that direction they undergo. The underlying characteristics of the BGC parameter Ψ X t , t are investigated by examining its geometric properties. The most appropriate convex form for Ψ , that is, the parabolic cylinder is identified after extensive simulation of various possible forms. The formula for the resulting hidden reflective barrier(s) is determined by comparing it with the simpler Ornstein–Uhlenbeck process (OUP). Applications of BGCSP arise when a series of semipermeable barriers are present, such as regulating interest rates and chemical reactions under concentration gradients, which gives rise to two hidden reflective barriers.

The Demand For Money in Pakistan: Reply (Notes and Comments)

1975 ◽  
Vol 14 (3) ◽  
pp. 370-375
Author(s):  
M. A. Akhtar
Keyword(s):  
Interest Rates ◽  
Money Demand ◽  
Strong Support ◽  
Physical Capital ◽  
Careful Examination ◽  
Demand For Money ◽  
Weak Support ◽  
Complementarity Hypothesis ◽  
The Difference ◽  
The One

I am grateful to Abe, Fry, Min, Vongvipanond, and Yu (hereafter re¬ferred to as AFMVY) [1] for obliging me to reconsider my article [2] on the demand for money in Pakistan. Upon careful examination, I find that the AFMVY results are, in parts, misleading and that, on the whole, they add very little to those provided in my study. Nevertheless, the present exercise as well as the one by AFMVY is useful in that it furnishes us with an opportunity to view some of the fundamental problems involved in an empi¬rical analysis of the demand for money function in Pakistan. Based on their elaborate critique, AFMVY reformulate the two hypo¬theses—the substitution hypothesis and the complementarity hypothesis— underlying my study and provide us with some alternative estimates of the demand for money in Pakistan. Briefly their results, like those in my study, indicate that income and interest rates are important in deter¬mining the demand for money. However, unlike my results, they also suggest that the price variable is a highly significant determinant of the money demand function. Furthermore, while I found only a weak support for the complementarity between money demand and physical capital, the results obtained by AFMVY appear to yield a strong support for that rela¬tionship.1 The difference in results is only a natural consequence of alter¬native specifications of the theory and, therefore, I propose to devote most of this reply to the criticisms raised by AFMVY and the resulting reformulation of the two mypotheses.

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

scholarly journals Using the Ornstein–Uhlenbeck process to model the evolution of interacting populations

2017 ◽  
Vol 429 ◽  
pp. 35-45 ◽  
Author(s):  
Krzysztof Bartoszek ◽  
Sylvain Glémin ◽  
Ingemar Kaj ◽  
Martin Lascoux
Keyword(s):  
Uhlenbeck Process ◽  
Interacting Populations ◽  
Ornstein Uhlenbeck Process
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