Narrow Results

The study aims to examine the Feldstein–Horioka puzzle in the Indian context during 2002Q2 to 2019Q4 to unearth nonlinear patterns in the data. Findings from an augmented Markov regime-switching model reveal two distinct, yet random regimes for correlations between savings and investment-GDP ratios, with higher correlation between the variables persisting for a longer duration. In the low correlation regime, trade-related factors, policy uncertainty and global shocks have a significant impact on the correlation. Fiscal shocks and trade costs explain high correlations in regime 2, while global shocks act to decrease the correlation in this regime. The high correlation regime dominates the study period and indicates that the Feldstein–Horioka puzzle of limited capital mobility persists in India. Economic agents appear to respond rapidly to changing domestic and global policy conditions, besides being affected by incomplete integration of goods markets, explaining the pattern of correlations.

This paper investigates ways of identifying and predicting currency crises in world-wide markets, with special focus on 1997 and 2008 currency crises. A novel Markov switching method is proposed for identifying currency crisis based on two states model, the turmoil state and tranquil state, which is the most suitable model considering the balance between model performance and computational demand. Compared with previous Markov switching currency crisis studies, the contribution of this paper comes from several ways. First, the dependent variable is different. While other papers use the exchange rate directly or the estimation of devaluation probability, this study uses the market pressure index calculated from nominal exchange rate and foreign reserves. Secondly, we allow different volatilities in different states, whereas other papers assume the same volatility in two states. Thirdly, our transition probabilities are constant rather than time-varying. The model shows evidence of state switching before crisis in many different currency markets. Lastly, we compare the Markov switching method with the widely used probit model which proposed an early warning system in terms of forecasting performance, and the empirical results show that the novel Markov switching method performs better than the probit model.

In this article, the dependence structure of the asset classes stocks, government bonds, and corporate bonds in different market environments and its implications on asset management are investigated for the US, European, and Asian market. Asset returns are modelled by a Markov-switching model which allows for two market regimes with completely different risk-return structures. Using major stock indices from all three regions, calm and turbulent market periods are identified for the time period between 1987 and 2009 and the correlation structures in the respective periods are compared. It turns out that the correlations between as well as within the asset classes under investigation are far from being stable and vary significantly between calm and turbulent market periods as well as in time. It also turns out that the US and European markets are much more integrated than the Asian and US/European ones. Moreover, the Asian market features more and longer turbulence phases. Finally, the impact of these findings is examined in a portfolio optimization context. To accomplish this, a case study using the mean-variance and the mean-conditional-value-at-risk framework as well as two levels of risk aversion is conducted. The results show that an explicit consideration of different market conditions in the modelling framework yields better portfolio performance as well as lower portfolio risk compared to standard approaches. These findings hold true for all investigated optimization frameworks and risk-aversion levels.

A higher dimensional Markov switching position dependent random map is a random map where the probabilities of switching from one higher dimension transformation to another are the entries of a stochastic matrix and the entries of stochastic matrix are functions of positions. In this note, we prove sufficient conditions for the existence of absolutely continuous measures for a class of higher dimensional Markov switching position dependent random maps. Our result is a generalization of the result in [Bahsoun & Góra, 2005; Bahsoun et al., 2005].

Infectious disease outbreaks have caused significant losses to populations worldwide in terms of morbidity, social and economic costs. This has prompted governments to seek suitable intervention policies to suppress the outbreaks. This paper aims to explore the intrinsic impact of intervention strategies and the psychological behavior of people on the spread of infectious diseases. Employing the finite state Markov chain, we formulate a new stochastic SIS epidemic model under regime switching by using the Beddington–DeAngelis transmission function, in the presence of some governmental control measures. The study of the model is centered on three different scenarios in terms of varying two control parameters. We analyze the deterministic system for the global dynamics in terms of basic reproductive number. Some new threshold parameters are defined to discuss the extinction and the persistence of the disease in the stochastic setting. Numerical assessments were undertaken to validate theoretical findings for the deterministic and stochastic systems. Our findings strongly suggest that heightened awareness among susceptible individuals contributes significantly to the eradication of infection and fosters a stable epidemiological situation. As levels of public awareness increase, particularly within the susceptible population, a discernible trend toward the eradication of the infection emerges, ultimately ensuring sustained stability within the epidemiological landscape.

Numerous incidents in the financial world have exposed the need for the design and analysis of models for correlated default timings. Some models have been studied in this regard which can capture the feedback in case of a major credit event. We extend the research in the same direction by proposing a new family of models having the feedback phenomena and capturing the effects of regime switching economy on the market. The regime switching economy is modeled by a continuous time Markov chain. The Markov chain may also be interpreted to represent the credit rating of the firm whose bond we seek to price. We model the default intensity in a pool of firms using the Markov chain and a risk factor process. We price some single-name and multi-name credit derivatives in terms of certain transforms of the default and loss processes. These transforms can be calculated explicitly in case the default intensity is modeled as a linear function of a conditionally affine jump diffusion process. In such a case, under suitable technical conditions, the price of credit derivatives are obtained as solutions to a system of ODEs with weak coupling, subject to appropriate terminal conditions. Solving the system of ODEs numerically, we analyze the credit derivative spreads and compare their behavior with the nonswitching counterparts. We show that our model can easily incorporate the effects of business cycle. We demonstrate the impact on spreads of the inclusion of rare states that attempt to capture a tight liquidity situation. These states are characterized by low floating interest rate, high default intensity rate, and high volatility. We also model the effects of firm restructuring on the credit spread, in case of a default.

We consider a stochastic-factor financial model wherein the asset price and the stochastic-factor processes depend on an observable Markov chain and exhibit an affine structure. We are faced with a finite investment horizon and derive optimal dynamic investment strategies that maximize the investor's expected utility from terminal wealth. To this end we apply Merton's approach, because we are dealing with an incomplete market. Based on the semimartingale characterization of Markov chains, we first derive the Hamilton–Jacobi–Bellman (HJB) equations that, in our case, correspond to a system of coupled nonlinear partial differential equations (PDE). Exploiting the affine structure of the model, we derive simple expressions for the solution in the case with no leverage, i.e. no correlation between the Brownian motions driving the asset price and the stochastic factor. In the presence of leverage, we propose a separable ansatz that leads to explicit solutions. General verification results are also proved. The results are illustrated for the special case of a Markov-modulated Heston model.

In this paper, we consider some properties of switching Brownian motion. Combining the analytic method and probabilistic method, some explicit expressions of density functions, the mean exit time and Laplace transform of exit time are given. This paper reveals how drift coefficients impact the first passage probabilities, scale functions and the mean exit time for switching Brownian motion.

A finite-state Markov chain is introduced in the noise terms of the three-dimensional stochastic Navier–Stokes equations in order to allow for transitions between two types of multiplicative noises. We call such systems as stochastic Navier–Stokes equations with Markov switching. To solve such a system, a family of regularized stochastic systems is introduced. For each such regularized system, the existence of a unique strong solution (in the sense of stochastic analysis) is established by the method of martingale problems and pathwise uniqueness. The regularization is removed in the limit by obtaining a weakly convergent sequence from the family of regularized solutions, and identifying the limit as a solution of the three-dimensional stochastic Navier–Stokes equation with Markov switching.

The fact that the relationships among the returns of financial assets tend to be nonlinear and time-varying has important implications for asset allocation. To describe these two features, this paper first combines a copula function with the Markov switching technique to model the dependence structure across assets and then builds on this Markov Switching Copula model to present a procedure for the timing of portfolio adjustments. Our empirical evidence confirms that the dependence structure between high-risk and low-risk stocks in the Shanghai and Shenzhen markets is not static but switches between regimes over the course of the sample horizon considered in this paper. More importantly, as a result of such regime-switching characteristics of their dependence structure, our analysis of the out-of-sample asset allocation performance indicates that employing the procedure proposed in this paper to identify regime changes and decide when to adjust portfolio weights allows investors with the Constant Relative Risk Aversion utility to achieve both higher realized returns and higher certainty equivalent rate of returns than does the use of strategies based on static models.

The purpose of this work is to investigate the asymptotic properties of a stochastic Gilpin–Ayala population system under regime switching on patches. We establish the global stability and the extinction of the trivial equilibrium state of the model. Furthermore, we show the existence of the stationary distribution for our system model. The analytical results are illustrated by computer simulations.

This contribution probes into ergodic stationary distribution for two stochastic SVELIT (susceptible-vaccinated-early latent-late latent-infective-treated) tuberculosis (TB) models to observe the impact of white noises and color noises on TB control in random environments. We first investigate the existence and uniqueness of ergodic stationary distribution (EUESD) for the autonomous SVELIT model subject to white noises via the proper Lyapunov functions, and sufficient conditions on the extinction of disease are acquired. Next, sufficient conditions for the EUESD and the extinction of disease for the SVELIT model with Markov switching are also established. Eventually, some numerical examples validate the theoretical findings. What’s more, it has been observed that higher amplitude noises may lead to the eradication of TB, which is conducive to TB control.

The stochastic switching SIR epidemic model with saturated incidence and limited medical treatment is investigated in this paper. By using Lyapunov methods and Itô formula, we first prove that the system has a unique global positive solution with any positive initial value. Then combining inequality technique and the ergodic property of Markov switching, the sufficient conditions for extinction and persistence in the mean of the disease are established. The results demonstrate that increasing medical resources and improving supply efficiency can accelerate the transition from the persistent state to the extinct state. Meanwhile, the high incidence rate will slow down the extinction of the disease. Specially, the switching noise can induce the system to toggle between the extinct and persistent states. Finally, some numerical simulations are carried out to confirm the analytical results.

This study investigates whether energy futures provide the ability to hedge against inflation. Using a Markov-switching vector error correction model (MS-VECM), we find that the Brent crude oil futures index is the only index that exhibits significant inflation hedging capability, among the subindexes of energy futures. Moreover, its inflation hedging capacity exhibits substantial variation over time, with most of the hedging power emerging under the relatively longer and more common regime. Results are robust to include common stocks and bonds in the model. We do not find evidence that unleaded gas, heating oil, gas oil, and natural gas futures have inflation hedging ability. Overall, our results suggest that crude oil futures are alternative candidates for well-diversified investment portfolios with inflation protection ability.