scholarly journals The Continuous-Time Ehrenfest Process in Term Structure Modelling

2010 ◽  
Vol 47 (03) ◽  
pp. 693-712
Author(s):  
A. Kaplun
Keyword(s):  
Term Structure ◽  
Continuous Time ◽  
Numerical Results ◽  
Vasicek Model ◽  
Finite State

In this paper, a finite-state mean-reverting model for the short rate, based on the continuous-time Ehrenfest process, will be examined. Two explicit pricing formulae for zero-coupon bonds will be derived in the general and special symmetric cases. Its limiting relationship to the Vasicek model will be examined with some numerical results.

scholarly journals The Continuous-Time Ehrenfest Process in Term Structure Modelling

2010 ◽  
Vol 47 (3) ◽  
pp. 693-712
Author(s):  
A. Kaplun
Keyword(s):  
Term Structure ◽  
Continuous Time ◽  
Numerical Results ◽  
Vasicek Model ◽  
Finite State

In this paper, a finite-state mean-reverting model for the short rate, based on the continuous-time Ehrenfest process, will be examined. Two explicit pricing formulae for zero-coupon bonds will be derived in the general and special symmetric cases. Its limiting relationship to the Vasicek model will be examined with some numerical results.

On quasi-stationary distributions in absorbing continuous-time finite Markov chains

1967 ◽  
Vol 4 (1) ◽  
pp. 192-196 ◽  
Author(s):  
J. N. Darroch ◽  
E. Seneta
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Continuous Time ◽  
Present Note ◽  
Time Parameter ◽  
Stationary Distributions ◽  
Finite State ◽  
Absorbing Markov Chains ◽  
Finite Markov Chains ◽  
Finite State Space

In a recent paper, the authors have discussed the concept of quasi-stationary distributions for absorbing Markov chains having a finite state space, with the further restriction of discrete time. The purpose of the present note is to summarize the analogous results when the time parameter is continuous.

scholarly journals Conditioning an additive functional of a Markov chain to stay nonnegative. I. Survival for a long time

2005 ◽  
Vol 37 (4) ◽  
pp. 1015-1034 ◽  
Author(s):  
Saul D. Jacka ◽  
Zorana Lazic ◽  
Jon Warren
Keyword(s):  
Markov Chain ◽  
Weak Convergence ◽  
State Space ◽  
Continuous Time ◽  
Additive Functional ◽  
Finite State ◽  
Long Time ◽  
Negative Drift ◽  
Irreducible Markov Chain ◽  
Finite State Space

Let (Xt)t≥0 be a continuous-time irreducible Markov chain on a finite state space E, let v be a map v: E→ℝ\{0}, and let (φt)t≥0 be an additive functional defined by φt=∫0tv(Xs)d s. We consider the case in which the process (φt)t≥0 is oscillating and that in which (φt)t≥0 has a negative drift. In each of these cases, we condition the process (Xt,φt)t≥0 on the event that (φt)t≥0 is nonnegative until time T and prove weak convergence of the conditioned process as T→∞.

scholarly journals Asymptotic results for the first and second moments and numerical computations in discrete-time bulk-renewal process

2019 ◽  
Vol 29 (1) ◽  
pp. 135-144
Author(s):  
James Kim ◽  
Mohan Chaudhry ◽  
Abdalla Mansur
Keyword(s):  
Discrete Time ◽  
Renewal Process ◽  
Generating Functions ◽  
Continuous Time ◽  
Constant Term ◽  
Numerical Results ◽  
Asymptotic Results ◽  
Numerical Computations ◽  
Second Moments ◽  
Simplified Solution

This paper introduces a simplified solution to determine the asymptotic results for the renewal density. It also offers the asymptotic results for the first and second moments of the number of renewals for the discrete-time bulk-renewal process. The methodology adopted makes this study distinguishable compared to those previously published where the constant term in the second moment is generated. In similar studies published in the literature, the constant term is either missing or not clear how it was obtained. The problem was partially solved in the study by Chaudhry and Fisher where they provided a asymptotic results for the non-bulk renewal density and for both the first and second moments using the generating functions. The objective of this work is to extend their results to the bulk-renewal process in discrete-time, including some numerical results, give an elegant derivation of the asymptotic results and derive continuous-time results as a limit of the discrete-time results.

A Fluid EOQ Model with Markovian Environment

2015 ◽  
Vol 52 (02) ◽  
pp. 473-489
Author(s):  
Yonit Barron
Keyword(s):  
Continuous Time ◽  
Inventory Level ◽  
Continuous Time Markov Chain ◽  
Holding Costs ◽  
Eoq Model ◽  
Long Run ◽  
Average Criterion ◽  
Production Inventory ◽  
Finite State ◽  
Cost Functionals

We consider a production-inventory model operating in a stochastic environment that is modulated by a finite state continuous-time Markov chain. When the inventory level reaches zero, an order is placed from an external supplier. The costs (purchasing and holding costs) are modulated by the state at the order epoch time. Applying a matrix analytic approach, fluid flow techniques, and martingales, we develop methods to obtain explicit equations for these cost functionals in the discounted case and under the long-run average criterion. Finally, we extend the model to allow backlogging.

HEDGING OPTIONS IN A DOUBLY MARKOV-MODULATED FINANCIAL MARKET VIA STOCHASTIC FLOWS

2019 ◽  
Vol 22 (08) ◽  
pp. 1950047 ◽  
Author(s):  
TAK KUEN SIU ◽  
ROBERT J. ELLIOTT
Keyword(s):  
Markov Chain ◽  
Financial Market ◽  
Continuous Time ◽  
Regime Switching ◽  
Stochastic Flows ◽  
Finite State ◽  
Markov Modulated ◽  
Appreciation Rate ◽  
The Interest Rate ◽  
Over Time

The hedging of a European-style contingent claim is studied in a continuous-time doubly Markov-modulated financial market, where the interest rate of a bond is modulated by an observable, continuous-time, finite-state, Markov chain and the appreciation rate of a risky share is modulated by a continuous-time, finite-state, hidden Markov chain. The first chain describes the evolution of credit ratings of the bond over time while the second chain models the evolution of the hidden state of an underlying economy over time. Stochastic flows of diffeomorphisms are used to derive some hedge quantities, or Greeks, for the claim. A mixed filter-based and regime-switching Black–Scholes partial differential equation is obtained governing the price of the claim. It will be shown that the delta hedge ratio process obtained from stochastic flows is a risk-minimizing, admissible mean-self-financing portfolio process. Both the first-order and second-order Greeks will be considered.

A Fluid EOQ Model with Markovian Environment

2015 ◽  
Vol 52 (02) ◽  
pp. 473-489 ◽  
Author(s):  
Yonit Barron
Keyword(s):  
Continuous Time ◽  
Inventory Level ◽  
Continuous Time Markov Chain ◽  
Holding Costs ◽  
Eoq Model ◽  
Long Run ◽  
Average Criterion ◽  
Production Inventory ◽  
Finite State ◽  
Cost Functionals

We consider a production-inventory model operating in a stochastic environment that is modulated by a finite state continuous-time Markov chain. When the inventory level reaches zero, an order is placed from an external supplier. The costs (purchasing and holding costs) are modulated by the state at the order epoch time. Applying a matrix analytic approach, fluid flow techniques, and martingales, we develop methods to obtain explicit equations for these cost functionals in the discounted case and under the long-run average criterion. Finally, we extend the model to allow backlogging.

CREDIT CONTAGION: PRICING CROSS-COUNTRY RISK IN BRADY DEBT MARKETS

2001 ◽  
Vol 04 (06) ◽  
pp. 921-938 ◽  
Author(s):  
MARCO AVELLANEDA ◽  
LIXIN WU
Keyword(s):  
Continuous Time ◽  
Credit Derivatives ◽  
Country Risk ◽  
Continuous Time Model ◽  
Time Model ◽  
Finite State ◽  
Defaultable Securities ◽  
Contagion Model ◽  
Cross Country ◽  
Credit Contagion

Credit contagion means that the credit deterioration of an entity causes the credit deterioration of other entities. In this paper, we build and test a continuous-time model for defaultable securities using a diffusive process for risk-free interest rate, and a finite-state continuous-time Markov process for the correlation of credit. The credit contagion, in particular, is established by relating transition rates of various credit states. Examples of derivative pricing with calibrated credit contagion model are provided. Initial empirical results with the benchmarks of Brady bonds show that our model is a viable new technique for the pricing and risk-managing of credit derivatives.

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