We investigate an optimal stopping problem for the expected value of a discounted payoff on a regime-switching geometric Brownian motion under two constraints on the possible stopping times: only at exogenous random times, and only during a specific regime. The main objectives are to show that an optimal stopping time exists as a threshold type and to derive expressions for the value functions and the optimal threshold. To this end, we solve the corresponding variational inequality and show that its solution coincides with the value functions. Some numerical results are also introduced. Furthermore, we investigate some asymptotic behaviors.

We derive an analytical approximation for the price of a credit default swap (CDS) contract under a regime-switching Black–Scholes model. To achieve this, we first derive a general formula for the CDS price, and establish the relationship between the unknown no-default probability and the price of a down-and-out binary option written on the same reference asset. Then we present a two-step procedure: the first step assumes that all the future information of the Markov chain is known at the current time and presents an approximation for the conditional price under a time-dependent Black–Scholes model, based on which the second step derives the target option pricing formula written in a Fourier cosine series. The efficiency and accuracy of the newly derived formula are demonstrated through numerical experiments.

In this study, we consider option pricing under a Markov regime-switching GARCH-jump (RS-GARCH-jump) model. More specifically, we derive the risk neutral dynamics and propose a lattice algorithm to price European and American options in this framework. We also provide a method of parameter estimation in our RS-GARCH-jump setting using historical data on the underlying time series. To measure the pricing performance of the proposed algorithm, we investigate the convergence of the tree-based results to the true option values and show that this algorithm exhibits good convergence. By comparing the pricing results of RS-GARCH-jump model with regime-switching GARCH (RS-GARCH) model, GARCH-jump model, GARCH model, Black–Scholes (BS) model, and Regime-Switching (RS) model, we show that accommodating jump effect and regime switching substantially changes the option prices. The empirical results also show that the RS-GARCH-jump model performs well in explaining option prices and confirm the importance of allowing for both jump components and regime switching.

We consider the optimal portfolio and consumption problem for a jump-diffusion process with regime switching. Under the criterion of maximizing the expected discounted total utility of consumption, two methods, namely, the dynamic programming principle and the stochastic maximum principle, are used to obtain the optimal result for the general objective function, which is the solution to a system of partial differential equations. Furthermore, we investigate the power utility as a specific example and analyse the existence and uniqueness of the optimal solution. Under the constraints of no-short-selling and nonnegative consumption, closed-form expressions for the optimal strategy and the value function are derived. Besides, some comparisons between the optimal results for the jump-diffusion model and the pure diffusion model are carried out. Finally, we discuss our optimal results in some special cases.

Our aim is to find sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain. First, we study properties of the state indicator function and the state occupation measure of a Markov chain. In particular, we establish weak convergence of the state occupation measure under a scaling of the generator matrix. Then, relying on the connection between the state occupation measure and the Dynkin martingale, we provide sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure. We apply our results to derive diffusion limits for the Markov-modulated Erlang loss model and the regime-switching Cox–Ingersoll–Ross process.

Multiple equilibria arise in standard New Keynesian models when the nominal interest rate is set according to the Taylor rule and constrained by a zero lower bound (ZLB). One of these equilibria is deflationary and referred to as an expectations-driven liquidity trap (ELT) as it arises because of the de-anchoring of inflation expectations. This study demonstrates that a simple tax rule responding to inflation can prevent a liquidity trap from arising without increasing government spending or debt. We analytically investigate the necessary and sufficient conditions to prevent an ELT and show that both the frequency and persistence of ELT episodes affect the extent to which the tax rule must respond to inflation. In brief, the higher the frequency or the longer the persistence of the ELT, the greater the response of the tax rate must be.

We investigate the long-time behavior of the Ornstein–Uhlenbeck process driven by Lévy noise with regime switching. We provide explicit criteria on the transience and recurrence of this process. Contrasted with the Ornstein–Uhlenbeck process driven simply by Brownian motion, whose stationary distribution must be light-tailed, both the jumps caused by the Lévy noise and the regime switching described by a Markov chain can derive the heavy-tailed property of the stationary distribution. The different role played by the Lévy measure and the regime-switching process is clearly characterized.

This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed, we assume that they follow a regime-switching Markov chain. For this model, we (1) give finite sample bounds on the expected occupancy probabilities, and (2) provide detailed asymptotics in the case where the underlying distribution is regularly varying. We find that in the regularly varying case the finite sample bounds are rate optimal and have, up to a constant, the same rate of decay as the asymptotic result.

We develop an N-regime Markov-switching model in which the latent state variable driving the regime switching is endogenously determined with the model disturbance term. The models structure captures a wide variety of patterns of endogeneity and yields a simple test of the null hypothesis of exogenous switching. We derive an iterative filter that generates objects of interest, including the model likelihood function and estimated regime probabilities. Using simulation experiments, we demonstrate that the maximum likelihood estimator performs well in finite samples and that a likelihood ratio test of exogenous switching has good size and power properties. We provide results from two applications of the endogenous switching model: a three-state model of US business cycle dynamics and a three-state volatility model of US equity returns. In both cases, we find statistically significant evidence in favor of endogenous switching.

In this paper we study a finite-fuel two-dimensional degenerate singular stochastic control problem under regime switching motivated by the optimal irreversible extraction problem of an exhaustible commodity. A company extracts a natural resource from a reserve with finite capacity and sells it in the market at a spot price that evolves according to a Brownian motion with volatility modulated by a two-state Markov chain. In this setting, the company aims at finding the extraction rule that maximizes its expected discounted cash flow, net of the costs of extraction and maintenance of the reserve. We provide expressions for both the value function and the optimal control. On the one hand, if the running cost for the maintenance of the reserve is a convex function of the reserve level, the optimal extraction rule prescribes a Skorokhod reflection of the (optimally) controlled state process at a certain state and price-dependent threshold. On the other hand, in the presence of a concave running cost function, it is optimal to instantaneously deplete the reserve at the time at which the commodity's price exceeds an endogenously determined critical level. In both cases, the threshold triggering the optimal control is given in terms of the optimal stopping boundary of an auxiliary family of perpetual optimal selling problems with regime switching.

Recent papers point to the problem that inflation-targeting models do not as of yet consider financial market stability that can considerably derail inflation-targeting monetary policy, implying significant nonzero crisis probabilities that could come along with large negative output and employment gaps. Credit flows and the instability of credit appear to be at the root of the financial instability problem. On the other hand, some authors recently questioned whether a too early and too strong leaning against the wind policy by central banks might have higher costs than benefits in terms of output and employment losses. In our paper, we include in an inflation targeting model a financial stabilization goal. In contrast to infinite horizon and two-period models, we propose a finite horizon model. The model is solved by using a new global solution algorithm, called Nonlinear Model Predictive Control (NMPC), exploring stabilizing/destabilizing effects of price and nonprice (credit volume) drivers of the output gap, inflation, and credit flows. We substantiate the theoretical part of the paper by approaching the subject empirically, relying to that end on a regime-switching structural vector autoregressive (VAR) for the euro area. The empirical model contains standard macroeconomic variables along with credit flows and loan interest rates, the central bank policy rate, and European Central Bank (ECB) balance sheet variables. The regime-switching feature of the model is meant to capture the state-dependent relationship between the variables, with specific nonlinearities having direct counterparts in the theoretical model. Based on a sign restriction methodology, we explore conventional and unconventional monetary policy shocks, loan supply, and demand shocks, under different regime assumptions to reveal the state-dependent effects of both interest rate and volume-based policies. The empirical results are used as guidance for the calibration of the theoretical model variants.

This paper analyzes the dynamical properties of monetary models with regime switching. We start with the analysis of the evolution of inflation when policy is guided by a simple monetary rule where coefficients switch with the policy regime. We rule out the possibility of a Hopf bifurcation and demonstrate the possibility of a period-doubling bifurcation. As a result, a small change in the parameters (e.g., a more active policy response) can lead to a drastic change in the path of inflation. We show that the New Keynesian model with a current-looking Taylor rule is not prone to bifurcations. A New Keynesian model with a hybrid rule, however, exhibits the same pattern of period-doubling bifurcations as the analysis with a simple monetary rule.

In this paper we consider an Ornstein–Uhlenbeck (OU) process (M(t))t≥0 whose parameters are determined by an external Markov process (X(t))t≥0 on a finite state space {1, . . ., d}; this process is usually referred to as Markov-modulated Ornstein–Uhlenbeck. We use stochastic integration theory to determine explicit expressions for the mean and variance of M(t). Then we establish a system of partial differential equations (PDEs) for the Laplace transform of M(t) and the state X(t) of the background process, jointly for time epochs t = t1, . . ., tK. Then we use this PDE to set up a recursion that yields all moments of M(t) and its stationary counterpart; we also find an expression for the covariance between M(t) and M(t + u). We then establish a functional central limit theorem for M(t) for the situation that certain parameters of the underlying OU processes are scaled, in combination with the modulating Markov process being accelerated; interestingly, specific scalings lead to drastically different limiting processes. We conclude the paper by considering the situation of a single Markov process modulating multiple OU processes.

In this paper we study the optimal dividend payments for a company of limited liability whose cash reserves in the absence of dividends follow a Markov-modulated jump-diffusion process with positive drifts and negative exponential jumps, where parameters and discount rates are modulated by a finite-state irreducible Markov chain. The main aim is to maximize the expected cumulative discounted dividend payments until bankruptcy time when cash reserves are nonpositive for the first time. We extend the results of Jiang and Pistorius [15] to our setup by proving that it is optimal to adopt a modulated barrier strategy at certain positive regime-dependent levels and that the value function can be explicitly characterized as the fixed point of a contraction.

The capacity of global agricultural production to meet increased demand for food from population growth and wealth accumulation is threatened by extensive land degradation. Nonetheless, previous research has focused primarily on the dynamic implications of input management and ignored land-use choice. This paper extends this theory through an examination of the intertemporal management of agricultural land through the use of non-crop inputs, such as fertilizer, and land uses that either degrade or restore productivity. The need to consider the relative total asset value of alternative crops over time is demonstrated. Moreover, higher output prices for degrading crops are shown to increase their relative value, motivating the later adoption of substitutes. An inability of land markets to reflect differences in resource quality and low capital malleability promote greater degradation. However, substitution of complementary effects through input use may help to sustain productivity. These factors are discussed in the context of crop sequence management in Western Australian cropping systems.

We propose a regime-switching model that allows demand to respond asymmetrically to upward and downward advertising changes. With the introduction of a smooth transition function, the model features smooth rather than abrupt parameter changes between regimes. We apply the model to nonalcoholic beverage data in the United States for 1974 through 2005 to investigate asymmetric advertising response. Results indicate that a decrease in milk advertising had a more profound impact on milk demand than an increase did. An increase in milk advertising had no impact on milk demand, but a decrease could have an own-advertising elasticity up to 0.049.

A regime-switching model for analysis of market integration has been developed that incorporates rate of trade information. An application of the methods to United States–China soybean trade demonstrates that the extended trade information allows better interpretation of market conditions. While the empirical results show that China's reform efforts since mid 1990s toward an open market have greatly improved United States–China soybean markets integration, about 40% of nontransitional disequilibrium occurrences likely indicate infrastructural limits such as the lack of information availability and limited competition. The United States–China price linkage is observed to be closer after China's World Trade Organization membership. The link has also been found relatively slack during the South American soybean harvest.

Term premia are shown to provide crucial information for discriminating among alternative sources of change in the economy, namely shifts in the variance of structural shocks and in monetary policy. These sources have been identified as competing explanations for time-varying features of major industrial economies during the 1980s and 1990s. Although hardly distinguishable through the lens of standard dynamic stochastic general equilibrium (DSGE) models, lower nonpolicy shock variances and “tighter” monetary policy regimes imply higher and lower term premia, respectively. As a result, moving to tighter monetary policy alone cannot explain the improved U.S. macroeconomic stability in the 1980s and 1990s: term premia would have shifted downward, a fact inconsistent with the evidence of higher premia from early 80s onward. Conversely, favorable shifts in nonpolicy innovation variance imply movements in term premia that are at least qualitatively consistent with historical patterns.