Markov repairable systems with stochastic regimes switching

Compared with the classical Markov repairable system, the Markov repairable system with stochastic regimes switching introduced in the paper provides a more realistic description of the practical system. The system can be used to model the dynamics of a repairable system whose performance regimes switch according to the external conditions. For example, to satisfy the demand variation that is typical for the power and communication systems and reduce the cost, these systems usually adjust their operating regimes. The transition rate matrices under distinct operating regimes are assumed to be different and the sojourn times in distinct regimes are governed by a finite state Markov chain. By using the theory of Markov process, Ion channel theory, and Laplace transforms, the up time of the system are studied. A numerical example is given to illustrate the obtained results. The effect of sojourn times in distinct regimes on the availability and the up time are also discussed in the numerical example.

Barrier Option Pricing in Regime Switching Models with Rebates

This paper is concerned with the valuation of single and double barrier knock-out call options in a Markovian regime switching model with specific rebates.The integral formulas of the rebates are derived via matrix Wiener-Hopf factorizations and Fourier transform techniques,also,the integral representations of the option prices are constructed.Moreover,the first-passage time density functions in two-state regime model are derived.As applications,several numerical algorithms and numerical examples are presented.

A Markov-switching dynamic regression analysis of the asymmetries related to the determinants of US crude oil production between 1982 and 2019

The structural changes brought about by shale oil revolution have inspired this paper of which the aim is to analyze the potential asymmetries related to the determinants of crude oil production in the USA.Thus,using a Markov-switching dynamic regression model in which parameters change when oil production moves from one regime to the other,it is found that for both oil production and oil relative importance,the regime that was dominant during the 1980s and the early 1990s when oil production in the USA was substantially high is the same regime that has once again become dominant in the decade corresponding to the shale oil revolution.Furthermore,the study reveals the existence of asymmetries in the relationship between US crude oil production and both manufacturing production and the consumer price index.Asymmetries are also found in the relationship between the relative importance US crude oil and manufacturing production.Finally,it is found that the intercept and the variance parameter also vary from one regime to the other,thus justifying the use of regime-dependent models.

永久性最低提取利益保证变额年金的公平保证费用定价

近年来,我国的人口老龄化趋势严重,截止到2012年底,年龄超过60岁的人口已达1.94亿,占总人口的14.3%,预计在2013年突破2亿。因此,老年人口的养老问题日益受到社会关注。在养老工具里面,相对于具有较低稳定收益的传统养老保险和没有最低保证的投连险,投资人(或投保人)更愿意选择具有最低利益保证的变额年金保险。在转移长寿风险的同时,投资人(或投保人)既有最低利益保证,又有可能获得更高的投资收益。因此有最低利益保证的变额年金未来会是年金保险的主流产品。本文对此进行探讨,为国内保险公司设计开发此类产品提供理论指导和参考。

MULTI-PERIOD MEAN-VARIANCE PORTFOLIO SELECTION WITH MARKOV REGIME SWITCHING AND UNCERTAIN TIME-HORIZON

This paper investigates a multi-period mean-variance portfolio selection with regime switching and uncertain exit time. The returns of assets all depend on the states of the stochastic market which are assumed to follow a discrete-time Markov chain. The authors derive the optimal strategy and the efficient frontier of the model in closed-form. Some results in the existing literature are obtained as special cases of our results.

Evidence on the Effects of Money Growth on Inflation with Regime Switching

Since the latter half of 2010, a new round of inflation has gradually been manifesting in China. The debate regarding whether excess money supply is responsible for this inflation has attracted scholars to investigate the effects of money growth on inflation. In this paper, we use correlation analysis to confirm the comovement between growth of monetary aggregates and inflation. We explore the asymmetric effects of monetary policy on inflation using the Markov regime-switching model The empirical results show that monetary policy can be more effective in curbing inflation in a high inflation state than in boosting the price level in a low inflation state. However, simply tightening the money supply might not be sufficient to suppress the price level To this end, the Chinese Government should adopt other policies, such as supply stabilization policies, to help suppress the price level Our study can help policy-makers to determine the actual economic state and provides some policy implications for the current inflation.

A model to determining the remaining useful life of rotating equipment,based on a new approach to determining state of degradation

Condition assessment is one of the most significant techniques of the equipment’s health management.Also,in PHM methodology cycle,which is a developed form of CBM,condition assessment is the most important step of this cycle.In this paper,the remaining useful life of the equipment is calculated using the combination of sensor information,determination of degradation state and forecasting the proposed health index.The combination of sensor information has been carried out using a new approach to determining the probabilities in the Dempster-Shafer combination rules and fuzzy c-means clustering method.Using the simulation and forecasting of extracted vibration-based health index by autoregressive Markov regime switching(ARMRS)method,final health state is determined and the remaining useful life(RUL)is estimated.In order to evaluate the model,sensor data provided by FEMTO-ST Institute have been used.

STOCK LOAN VALUATION UNDER A REGIME-SWITCHING MODEL WITH MEAN-REVERTING AND FINITE MATURITY

Stock loans are business contracts between borrowers and lenders in which the borroweruses shares of stock as collateral for the loan.Since the value of the collateral is subject to wide andfrequent price swings,valuing such a transaction behaves more like an option pricing problem thana debt valuation problem.This paper will list,prove,and analyze formulas for stock loan valuationwith finite horizon under various stock models,including classical geometric Brownian motion,meanreverting,and two-state regime-switching with both mean-reverting and geometric Brownian motionstates.Numerical examples are reported to illustrate the results.

Heavy tail and light tail of Cox-Ingersoll-Ross processes with regime-switching

This study aims to investigate the tail behavior of Cox-Ingersoll-Ross(CIR) processes with regime switching. An essential difference shown in this study between CIR processes with and without regime switching is that the stationary distribution of those with regime switching may be heavy-tailed. We first provide sharp criteria to justify the existence of a stationary distribution for the CIR process with regime switching, which is applied to study the long-term returns of interest rates. Then, we provide a criterion to identify whether this distribution is heavy-tailed. Our results provide theoretical evidence of the existence of regime switching for interest-rate models based on empirical evidence of a heavy-tailed distribution.

Asymptotically Optimal Dividend Policy for Regime-Switching Compound Poisson Models

This work develops asymptotically optimal dividend policies to maximize the expected present value of dividends until ruin.Compound Poisson processes with regime switching are used to model the surplus and the switching（a continuous-time controlled Markov chain） represents random environment and other economic conditions.Assuming the switching to be fast varying together with suitable conditions,it is shown that the system has a limit that is an average with respect to the invariant measure of a related Markov chain.Under simple conditions,the optimal policy of the limit dividend strategy is a threshold policy.Using the optimal policy of the limit system as a guide,feedback control for the original surplus is then developed.It is demonstrated that the constructed dividend policy is asymptotically optimal.

Time-Inconsistent Stochastic LQ Problem with Regime Switching

This paper investigates a time-inconsistent stochastic linear-quadratic problem with regime switching that is characterized via a finite-state Markov chain.Open-loop equilibrium control is studied in this paper whose existence is characterized via Markov-chain-modulated forward-backward stochastic difference equations and generalized Riccati-like equations with jumps.

Valuation and Hedging Strategy of Currency Options under Regime-Switching Jump-Diffusion Model

The main purpose of this thesis is in analyzing and empirically simulating risk minimizing European foreign exchange option pricing and hedging strategy when the spot foreign exchange rate is governed by a Markov-modulated jump-diffusion model. The domestic and foreign money market interest rates, the drift and the volatility of the exchange rate dynamics all depend on a continuous-time hidden Markov chain which can be interpreted as the states of a macro-economy. In this paper, we will provide a practical lognormal diffusion dynamic of the spot foreign exchange rate for market practitioners. We employing the minimal martingale measure to demonstrate a system of coupled partial-differential-integral equations satisfied by the currency option price and attain the corresponding hedging schemes and the residual risk. Numerical simulations of the double exponential jump diffusion regime-switching model are used to illustrate the different effects of the various parameters on currency option prices.

Stochastic Maximum Principle for Forward-Backward Regime Switching Jump Diffusion Systems and Applications to Finance

The authors prove a sufficient stochastic maximum principle for the optimal control of a forward-backward Markov regime switching jump diffusion system and show its connection to dynamic programming principle. The result is applied to a cash flow valuation problem with terminal wealth constraint in a financial market. An explicit optimal strategy is obtained in this example.

Risk-minimizing Hedging Strategy for an Equity-indexed Annuity under a Regime Switching Model

The equity-indexed annuity （EIA） contract offers a proportional participation in the performance of a specified equity index, in addition to a guaranteed return on the single premium. How to manage the risk of the EIA is an important issue. This paper considers the hedging of the EIA. We assume that the parameters of the financial model depend on a continuous-time finite-state Markov chain and the Markov chain is observed, that is the Markov regime switching model. The state of the Markov chain can be interpreted as the state of an economy. Under the regime switching model~ we obtain the risk-minimizing hedging strategy for the EIA.

Value-at-Risk Approach to Currency Crises： A Brazilian Example With the Central Bank and Currency Based Assets＊

This paper uses a Value at Risk （VaR） approach to evaluate a country financial vulnerability, by analyzing the risk exposure of its Central Bank, as if their assets are subject to market risk. The Brazilian currency exchange swaps contracts （USS/Brazilian Reais） are submitted to a delta-normal VaR method, in order to evaluate the market risk of each swaps series, by modeling the variance of the daily returns, from August 1999 to January 2003. All daily returns series exhibited heteroscedasticity in the conditional variance and sudden changes in the unconditional variance. The points of changes of the unconditional variance were determined through the Iterative Cumulative Sum of Squares （ICSS） algorithm, and the conditional variance was modeled with Markov-Switching-Generalized Autoregressive Conditional Heteroscedasticity （SWGARCH） in order to capture heteroscedasticity and regime change. The results lead to two main conclusions： First, a VaR model must incorporate heteroscedasticity and regime switching in order to describe the variance of the tested series, submitted to brisk changes of economic and political scenarios. Second, a volatility-based VaR do not necessarily generate forward-looking indicators, but rather coincident indicators of possible financial vulnerabilities. The future research will evolve towards evaluating the effects of the Basel III recommendations as if they could be applied to this crisis period.

A Markov Copula Model with Regime Switching and Its Application

Regime switching,which is described by a Markov chain,is introduced in a Markov copula model.We prove that the marginals（X,H^i）,i = 1,2,3 of the Markov copula model（X,H） are still Markov processes and have martingale property.In this proposed model,a pricing formula of credit default swap（CDS） with bilateral counterparty risk is derived.

Common Fixed Point Theorems and Q-property for Quasi-contractive Mappings under c-distance on TVS-valued Cone Metric Spaces without the Normality

In this paper, we derive the stochastic maximum principle for optimal control problems of the forward-backward Markovian regime-switching system. The control system is described by an anticipated forward-backward stochastic pantograph equation and modulated by a continuous-time finite-state Markov chain. By virtue of classical variational approach, duality method, and convex analysis, we obtain a stochastic maximum principle for the optimal control.

Regime Dependent Sensitivity of Country Exchange Traded Funds to Common Risk Factors

If common factors jointly affect country stock markets, it is an indica- tion of global stock market integration. Common factors may affect some markets more/less than other markets, an indication of the degree of global stock market in- tegration/segmentation. In this paper, we study the integration of global stock mar- kets based on the returns on exchange traded funds （ETFs） for the US, Canada, UK, Germany, France, Italy, Australia and Japan. The relationship between country ETF returns and common risk factors may be time-varying across countries, and that favors a regime switching （RS） factor model for the dynamics of the country ETF returns. A RS factor model for the relationship between country ETF returns and common risk factors is fitted to daily data for the period from May 31, 2000 to March 31, 2014. We use the data to test a hierarchy of hypotheses on country ETF returns： （1） common factor exposure across all country ETFs and all regimes; （2） common factor exposure across some country ETFs and all regimes, and （3） common factor exposure across some country ETFs and some regimes. The RS factor model for ETF returns fits the data well and the common factors have variable effects across countries and over regimes

Near-Optimal Controls of Differential Systems with Switching and Random Jumps Subject to Fast Switching and Wideband Noise Perturbation

This work develops near-optimal controls for systems given by differential equations with wideband noise and random switching.The random switching is modeled by a continuous-time,time-inhomogeneous Markov chain.Under broad conditions,it is shown that there is an associated limit problem,which is a switching jump diffusion.Using near-optimal controls of the limit system,we then build controls for the original systems.It is shown that such constructed controls are nearly optimal.

Liquidity of China’s government bond market: Measures and driving forces

We construct a daily liquidity index of China’s government bond market using transaction data from the national interbank market during 2001–2020.The index is a composite of popular price-based and quantity-based metrics of liquidity.The composite indices,ob-tained by averaging across different metrics and by applying the principal component analysis,respectively,both point to a better liquidity condition after 2010.Market liquidity swings appear to be highly correlated with domestic funding liquidity and financial mar-ket volatility,but display fewer correlations with global macrofinan-cial indicators.Our findings suggest that the further deepening of the government bond market would support domestic financial stability and monetary operations down the road.