Classical and Impulse Stochastic Control of the Exchange Rate Using Interest Rates and Reserves

Cadenillas, Abel; Zapatero, Fernando

doi:10.1111/1467-9965.00086

Cited by 92 publications

(76 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…As evident from Eqs. (7) to (10), this result does not depend on whether type 1 investors hold more or less of the GBP bond than type 2 investors, but on whether there is trading in this economy, i.e., X 1 6 = X 2 . 11 …”

Section: Dealersmentioning

confidence: 82%

“…9 Many competing dealers instead set the same quotes such that the expected profit for the representative MM is equal to zero, by virtue of Bertrand competition. 10 In order to isolate the impact of interventions on quotes and spreads, we assume that the MMs do not face any order processing costs or inventory control, i.e., that our stylized currency market is frictionless. Then, if we define M t as the information set available to the dealer(s) at time t, before the next incoming order arrives, S i,t as the price quoted to an investor of type i, and S CB t as the price quoted to the CB, the expected instantaneous profit Π t earned by the MM can be represented as…”

Section: Dealersmentioning

confidence: 99%

“…Nevertheless, we choose to use this simplified scenario to explain the basic intuition for how dealers adjust their quotes in response to the (likelihood of) arrival of a CB order, and to understand why the adjustment does (or does not) induce a change in the spreads with respect to the basic case of Eq. (6) to (10). In ,Section 4 we eventually introduce information asymmetry among agents regarding some of the model's parameters and more realistic assumptions for their information sets, and study the impact of interventions on the process of price formation when the signaling channel of effectiveness is active as well.…”

Section: The Full Information Casementioning

confidence: 99%

See 2 more Smart Citations

Central bank intervention and the intraday process of price formation in the currency markets

Pasquariello

2010

Journal of International Money and Finance

View full text Add to dashboard Cite

We study the impact of sterilized Central Bank interventions on the microstructure of currency markets. We analyze their major channels of effectiveness, imperfect substitutability and signaling, in a model of sequential trading in which the stylized monetary authority is a rational, but not necessarily profit-maximizing player. In such a setting, and consistent with available empirical evidence, we find that intervention has endogenous long-lived effects on quotes when informative about policy objectives and fundamentals, or when the threat of future actions by the Central Bank is significant and credible, for these circumstances lead uninformed investors or dealers to a permanent revision in their beliefs. Portfolio balance effects of such transactions are instead short-lived, because of trading occurring sequentially and not because of high asset substitutability, as often argued in the literature. We also find that a monetary authority attempting to lean against the wind or to chase the trend of the domestic currency is generally more successful when dealers compete against each other for the incoming trades. Intuitively, competition induces the dealers to pass all revenues or losses they expect from trading with the Central Bank onto the population of investors. This is accomplished by greater, and generally asymmetric, revisions of their bid and ask quotes. The resulting equilibrium process of intraday price formation and bid-ask spreads are shown to depend crucially on the degree of market power held by the forex dealers, on the sign and magnitude of announced and realized interventions, on the perceived likelihood of a future intervention to occur, and on the transparency of the order flow induced by the intervention.

show abstract

Section: Dealersmentioning

confidence: 82%

Section: Dealersmentioning

confidence: 99%

Section: The Full Information Casementioning

confidence: 99%

See 1 more Smart Citation

Central bank intervention and the intraday process of price formation in the currency markets

Pasquariello

2010

Journal of International Money and Finance

View full text Add to dashboard Cite

show abstract

“…The stochastic singular control problems have received considerable research attention in recent years due to wide applicability in a number of different areas, see for instance [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] . In most classical cases, the optimal singular control problem was investigated through dynamic programming principle.…”

Section: L(t)dξ(t)mentioning

confidence: 99%

Singular mean-field optimal control for forward-backward stochastic systems and applications to finance

Hafayed

2014

Int. J. Dynam. Control

View full text Add to dashboard Cite

In this paper, we study a class of singular stochastic optimal control problems for systems described by mean-field forward-backward stochastic differential equations, in which the coefficient depend not only on the state process but also its marginal law of the state process through its expected value. Moreover, the cost functional is also of mean-field type. The control variable has two components, the first being absolutely continuous and the second singular control. Necessary conditions for optimal control for this systems in the form of a Pontrygin maximum principle are established by means convex perturbation techniques for both continuous and singular parts. Our stochastic maximum principle differs from the classical one in the sense that here the adjoint equation has a mean-field type. The control domain is assumed to be convex. As an illustration of our results, we consider a mean-variance portfolio selection mixed with a recursive utility functional optimization problem involving singular control. The explicit expression of the optimal portfolio selection strategy is obtained in the state feedback form involving both state process and its marginal distribution, via the solutions of Riccati ordinary differential equations with time-inconsistent solution.Keywords Singular stochastic control · Mean-field forward-backward stochastic differential equation · Mean-field type maximum principle · Time-inconsistent control problem · McKean-Vlasov systems M. Hafayed

show abstract

“…Reinsurance has been long investigated as an intrinsic part of commercial insurance, of which the mainstream modeling framework is profit maximization with the one-sided impulse control of an underlying reserve process. There are two types of one-sided impulse control: downside-only impulse control (such as a dividend payment) with a fixed cost K  (e.g., Cadenillas et al [3], Hojgaard and Taksar [4]) and upside-only impulse control (such as inventory ordering) with a fixed cost K  (e.g., Bensoussan et al [2], Eisenberg and Schmidli [5], Sulem [6]). In this paper, we examine mutual proportional reinsurance-a mutual reserve system that is intended for the collective reinsurance needs of homogeneous mutual members, such as the P&I Clubs in marine mutual insurance (e.g., Yuan [7]) and the reserve banks in the US Federal Reserve (e.g., Dawande et al [8]).…”

Section: Introductionmentioning

confidence: 99%

Mixed Band Control of Mutual Proportional Reinsurance

Taksar¹,

Liu²,

Yuan³

2013

JMF

View full text Add to dashboard Cite

In this paper, we investigate the optimization of mutual proportional reinsurance-a mutual reserve system that is intended for the collective reinsurance needs of homogeneous mutual members, such as P&I Clubs in marine mutual insurance and reserve banks in the US Federal Reserve, where a mutual member is both an insurer and an insured. Compared to general (non-mutual) insurance models, which involve one-sided impulse control (i.e., either downside or upside impulse) of the underlying insurance reserve process that is required to be positive, a mutual insurance differs in allowing two-sided impulse control (i.e., both downside and upside impulse), coupled with the classical proportional control of reinsurance. We prove that a special band-type impulse control   , , , a A B b a with and a A coupled with a proportional reinsurance policy (classical control), is optimal when the objective is to minimize the total maintenance cost. That is, when the reserve position reaches a lower boundary of , the reserve should immediately be raised to level A; when the reserve reaches an upper boundary of b, it should immediately be reduced to a level B. An interesting finding produced by the study reported in this paper is that there exists a situation such that if the upside fixed cost is relatively large in comparison to a finite threshold, then the optimal band control is reduced to a downside only (i.e., dividend payment only) control in the form of   , B b 0, 0; with 0 a A   . In this case, it is optimal for the mutual insurance firm to go bankrupt as soon as its reserve level reaches zero, rather than to jump restart by calling for additional contingent funds. This finding partially explains why many mutual insurance companies, that were once quite popular in the financial markets, are either disappeared or converted to non-mutual ones.

show abstract

Classical and Impulse Stochastic Control of the Exchange Rate Using Interest Rates and Reserves

Cited by 92 publications

References 12 publications

Central bank intervention and the intraday process of price formation in the currency markets

Central bank intervention and the intraday process of price formation in the currency markets

Singular mean-field optimal control for forward-backward stochastic systems and applications to finance

Mixed Band Control of Mutual Proportional Reinsurance

Contact Info

Product

Resources

About