scholarly journals Optimal reduction of public debt under partial observation of the economic growth

2020 ◽  
Vol 24 (4) ◽  
pp. 1083-1132
Author(s):  
Giorgia Callegaro ◽  
Claudia Ceci ◽  
Giorgio Ferrari
Keyword(s):  
Optimal Stopping ◽  
Partial Observation ◽  
Full Information ◽  
Optimal Stopping Problem ◽  
Macroeconomic Conditions ◽  
Diffusive Dynamics ◽  
State Of The Economy ◽  
Finite State ◽  
The Government ◽  
Macroeconomic Indicator

Abstract We consider a government that aims at reducing the debt-to-(gross domestic product) (GDP) ratio of a country. The government observes the level of the debt-to-GDP ratio and an indicator of the state of the economy, but does not directly observe the development of the underlying macroeconomic conditions. The government’s criterion is to minimise the sum of the total expected costs of holding debt and of debt reduction policies. We model this problem as a singular stochastic control problem under partial observation. The contribution of the paper is twofold. Firstly, we provide a general formulation of the model in which the level of the debt-to-GDP ratio and the value of the macroeconomic indicator evolve as a diffusion and a jump-diffusion, respectively, with coefficients depending on the regimes of the economy. The latter are described through a finite-state continuous-time Markov chain. We reduce the original problem via filtering techniques to an equivalent one with full information (the so-called separated problem), and we provide a general verification result in terms of a related optimal stopping problem under full information. Secondly, we specialise to a case study in which the economy faces only two regimes and the macroeconomic indicator has a suitable diffusive dynamics. In this setting, we provide the optimal debt reduction policy. This is given in terms of the continuous free boundary arising in an auxiliary fully two-dimensional optimal stopping problem.

scholarly journals Sum the Multiplicative Odds to One and Stop

2010 ◽  
Vol 47 (03) ◽  
pp. 761-777 ◽  
Author(s):  
Mitsushi Tamaki
Keyword(s):  
Poisson Process ◽  
Optimal Stopping ◽  
Process Approach ◽  
Stopping Rule ◽  
Secretary Problem ◽  
Full Information ◽  
Bernoulli Trials ◽  
Optimal Stopping Problem ◽  
Asymptotic Results ◽  
Optimal Stopping Rule

We consider the optimal stopping problem of maximizing the probability of stopping on any of the last m successes of a sequence of independent Bernoulli trials of length n, where m and n are predetermined integers such that 1 ≤ m < n. The optimal stopping rule of this problem has a nice interpretation, that is, it stops on the first success for which the sum of the m-fold multiplicative odds of success for the future trials is less than or equal to 1. This result can be viewed as a generalization of Bruss' (2000) odds theorem. Application will be made to the secretary problem. For more generality, we extend the problem in several directions in the same manner that Ferguson (2008) used to extend the odds theorem. We apply this extended result to the full-information analogue of the secretary problem, and derive the optimal stopping rule and the probability of win explicitly. The asymptotic results, as n tends to ∞, are also obtained via the planar Poisson process approach.

On the full information best-choice problem

1996 ◽  
Vol 33 (3) ◽  
pp. 678-687 ◽  
Author(s):  
Alexander V. Gnedin
Keyword(s):  
Poisson Process ◽  
Optimal Stopping ◽  
Infinite Sequence ◽  
Full Information ◽  
Optimal Stopping Problem ◽  
Choice Problem ◽  
Best Choice Problem ◽  
Finite Problem

We introduce the optimal stopping problem of an infinite sequence of records associated with a planar Poisson process. This problem serves as a limiting form of the classical full information best-choice problem. A link between the finite problem and its limiting form is established via embedding n i.i.d. observations into the planar process.

scholarly journals Sum the Multiplicative Odds to One and Stop

2010 ◽  
Vol 47 (3) ◽  
pp. 761-777 ◽  
Author(s):  
Mitsushi Tamaki
Keyword(s):  
Poisson Process ◽  
Optimal Stopping ◽  
Process Approach ◽  
Stopping Rule ◽  
Secretary Problem ◽  
Full Information ◽  
Bernoulli Trials ◽  
Optimal Stopping Problem ◽  
Asymptotic Results ◽  
Optimal Stopping Rule

We consider the optimal stopping problem of maximizing the probability of stopping on any of the last m successes of a sequence of independent Bernoulli trials of length n, where m and n are predetermined integers such that 1 ≤ m < n. The optimal stopping rule of this problem has a nice interpretation, that is, it stops on the first success for which the sum of the m-fold multiplicative odds of success for the future trials is less than or equal to 1. This result can be viewed as a generalization of Bruss' (2000) odds theorem. Application will be made to the secretary problem. For more generality, we extend the problem in several directions in the same manner that Ferguson (2008) used to extend the odds theorem. We apply this extended result to the full-information analogue of the secretary problem, and derive the optimal stopping rule and the probability of win explicitly. The asymptotic results, as n tends to ∞, are also obtained via the planar Poisson process approach.

On the full information best-choice problem

1996 ◽  
Vol 33 (03) ◽  
pp. 678-687 ◽  
Author(s):  
Alexander V. Gnedin
Keyword(s):  
Poisson Process ◽  
Optimal Stopping ◽  
Infinite Sequence ◽  
Full Information ◽  
Optimal Stopping Problem ◽  
Choice Problem ◽  
Best Choice Problem ◽  
Finite Problem

We introduce the optimal stopping problem of an infinite sequence of records associated with a planar Poisson process. This problem serves as a limiting form of the classical full information best-choice problem. A link between the finite problem and its limiting form is established via embedding n i.i.d. observations into the planar process.

scholarly journals On a simple optimal stopping problem

1973 ◽  
Vol 5 (4) ◽  
pp. 297-312 ◽  
Author(s):  
William M. Boyce
Keyword(s):  
Optimal Stopping ◽  
Optimal Stopping Problem

The Relationship Between Government Popularity and Approval for the Government's Record in the United Kingdom

1985 ◽  
Vol 15 (2) ◽  
pp. 165-186 ◽  
Author(s):  
John Hudson
Keyword(s):  
The Public ◽  
The Past ◽  
The United Kingdom ◽  
State Of The Economy ◽  
Degree Of Stability ◽  
Key Variables ◽  
The Government ◽  
The Relationship ◽  
Opinion Polls

The past decade has seen the growth of a considerable literature on the link between government popularity, as reflected by the proportion of the public indicating their intention to vote for the government in opinion polls, and the state of the economy, as represented by certain key variables. The work began in the early 1970s with articles by Goodhart and Bhansali, Mueller, and Kramer. It continued through the decade; some of the more recent contributions can be found in a set of readings edited by Hibbs and Fassbender. However, despite the amount and quality of this work, problems remain. Principal amongst these, as Chrystal and Alt have pointed out, is the inability to estimate a relationship which exhibits any degree of stability either over time or between researchers. Nearly all the studies have been successful in finding a significant relationship for specific time periods, but when these are extended, or when the function is used to forecast outside the original estimation period, the relationship appears to break down.

A Note on a Lower Bound for the Multiplicative Odds Theorem of Optimal Stopping

2014 ◽  
Vol 51 (03) ◽  
pp. 885-889 ◽  
Author(s):  
Tomomi Matsui ◽  
Katsunori Ano
Keyword(s):  
Lower Bound ◽  
Optimal Stopping ◽  
Secretary Problem ◽  
Bernoulli Trials ◽  
Optimal Stopping Problem ◽  
Maximum Probability ◽  
Optimal Stopping Rule ◽  
Optimal Probability ◽  
Optimal Stopping Theory ◽  
Special Case

In this note we present a bound of the optimal maximum probability for the multiplicative odds theorem of optimal stopping theory. We deal with an optimal stopping problem that maximizes the probability of stopping on any of the last m successes of a sequence of independent Bernoulli trials of length N, where m and N are predetermined integers satisfying 1 ≤ m &lt; N. This problem is an extension of Bruss' (2000) odds problem. In a previous work, Tamaki (2010) derived an optimal stopping rule. We present a lower bound of the optimal probability. Interestingly, our lower bound is attained using a variation of the well-known secretary problem, which is a special case of the odds problem.

Sign in / Sign up

Export Citation Format

Share Document