scholarly journals A Class of Itô Diffusions with Known Terminal Value and Specified Optimal Barrier

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 123 ◽  
Author(s):  
Bernardo D’Auria ◽  
Alessandro Ferriero
Keyword(s):  
Insider Trading ◽  
Optimal Stopping ◽  
Stock Options ◽  
Optimization Problems ◽  
Brownian Bridge ◽  
A Priori ◽  
Stopping Time ◽  
Optimal Time ◽  
The One ◽  
Stopping Time Problems

In this paper, we study the optimal stopping-time problems related to a class of Itô diffusions, modeling for example an investment gain, for which the terminal value is a priori known. This could be the case of an insider trading or of the pinning at expiration of stock options. We give the explicit solution to these optimization problems and in particular we provide a class of processes whose optimal barrier has the same form as the one of the Brownian bridge. These processes may be a possible alternative to the Brownian bridge in practice as they could better model real applications. Moreover, we discuss the existence of a process with a prescribed curve as optimal barrier, for any given (decreasing) curve. This gives a modeling approach for the optimal liquidation time, i.e., the optimal time at which the investor should liquidate a position to maximize the gain.

scholarly journals OPTIMAL STOPPING WITH DELAYED INFORMATION

2005 ◽  
Vol 05 (02) ◽  
pp. 271-280 ◽  
Author(s):  
BERNT ØKSENDAL
Keyword(s):  
Optimal Stopping ◽  
Time Lag ◽  
Stopping Time ◽  
Resource Extraction ◽  
Optimal Time ◽  
Optimal Stopping Problem ◽  
Delayed Information ◽  
Optimal Resource ◽  
Flow Of Information ◽  
Strong Markov

We study a general optimal stopping problem for a strong Markov process in the case when there is a time lag δ > 0 from the time τ when the decision to stop is taken (a stopping time) to the time τ + δ when the system actually stops. Equivalently, we impose the constraint that the admissible times for stopping are stopping (Markov) times with respect to the delayed flow of information. It is shown that such a problem can be reduced to a classical optimal stopping problem by a simple transformation. The results are applied: (i) to find the optimal time to sell an asset (ii) to solve an optimal resource extraction problem, in both cases under delayed information flow.

Optimal Stopping Time for Geometric Random Walks with Power Payoff Function

2020 ◽  
Vol 81 (7) ◽  
pp. 1192-1210
Author(s):  
O.V. Zverev ◽  
V.M. Khametov ◽  
E.A. Shelemekh
Keyword(s):  
Random Walks ◽  
Optimal Stopping ◽  
Stopping Time ◽  
Payoff Function ◽  
Optimal Stopping Time

scholarly journals Minkowski box from Yangian bootstrap

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Luke Corcoran ◽  
Florian Loebbert ◽  
Julian Miczajka ◽  
Matthias Staudacher
Keyword(s):  
Minkowski Space ◽  
Wigner Function ◽  
Functional Form ◽  
A Priori ◽  
Alternative Methods ◽  
Feynman Integrals ◽  
The One

Abstract We extend the recently developed Yangian bootstrap for Feynman integrals to Minkowski space, focusing on the case of the one-loop box integral. The space of Yangian invariants is spanned by the Bloch-Wigner function and its discontinuities. Using only input from symmetries, we constrain the functional form of the box integral in all 64 kinematic regions up to twelve (out of a priori 256) undetermined constants. These need to be fixed by other means. We do this explicitly, employing two alternative methods. This results in a novel compact formula for the box integral valid in all kinematic regions of Minkowski space.

scholarly journals Risk Assessment of Circuit Breakers Using Influence Diagrams with Interval Probabilities

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 737
Author(s):  
Jelena D. Velimirovic ◽  
Aleksandar Janjic
Keyword(s):  
Power System ◽  
Predictive Modelling ◽  
Optimal Time ◽  
Influence Diagrams ◽  
Circuit Breakers ◽  
Interval Probability ◽  
Complex Power ◽  
Interval Width ◽  
Credal Sets ◽  
The One

This paper deals with uncertainty, asymmetric information, and risk modelling in a complex power system. The uncertainty is managed by using probability and decision theory methods. More specifically, influence diagrams—as extended Bayesian network functions with interval probabilities represented through credal sets—were chosen for the predictive modelling scenario of replacing the most critical circuit breakers in optimal time. Namely, based on the available data on circuit breakers and other variables that affect the considered model of a complex power system, a group of experts was able to assess the situation using interval probabilities instead of crisp probabilities. Furthermore, the paper examines how the confidence interval width affects decision-making in this context and eliminates the information asymmetry of different experts. Based on the obtained results for each considered interval width separately on the action to be taken over the considered model in order to minimize the risk of the power system failure, it can be concluded that the proposed approach clearly indicates the advantages of using interval probability when making decisions in systems such as the one considered in this paper.

scholarly journals Supergraph calculation of one-loop divergences in higher-derivative 6D SYM theory

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
I. L. Buchbinder ◽  
E. A. Ivanov ◽  
B. S. Merzlikin ◽  
K. V. Stepanyantz
Keyword(s):  
Effective Action ◽  
A Priori ◽  
Coupling Constant ◽  
Harmonic Superspace ◽  
Classical Action ◽  
Higher Derivative ◽  
Component Approach ◽  
Dimensionless Coupling ◽  
The One ◽  
Dimensionless Coupling Constant

Abstract We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of renormalizable 6D, $$ \mathcal{N} $$ N = (1, 0) supersymmetric higher-derivative gauge theory with a dimensionless coupling constant. Our consideration uses the background superfield method allowing to carry out the analysis of the effective action in a manifestly gauge covariant and $$ \mathcal{N} $$ N = (1, 0) supersymmetric way. We exploit the regularization by dimensional reduction, in which the divergences are absorbed into a renormalization of the coupling constant. Having the expression for the one-loop divergences, we calculate the relevant β-function. Its sign is specified by the overall sign of the classical action which in higher-derivative theories is not fixed a priori. The result agrees with the earlier calculations in the component approach. The superfield calculation is simpler and provides possibilities for various generalizations.

Insider Trading in Israel and England, Part II

1972 ◽  
Vol 7 (3) ◽  
pp. 373-410
Author(s):  
Aharon Yoran
Keyword(s):  
Insider Trading ◽  
The Other ◽  
Fiduciary Duties ◽  
The Law ◽  
The One

It is submitted that even if the hapless outsider cannot bring an action for damages because of the existing state of the law regarding fiduciary duties and breach of statutory duties, he still has an equitable remedy of rescission of the contract based on quasi-contractual principles. The crime of fraud, under secs. 13 and 54, respectively, would be made the basis of setting the contract (of sale or purchase) aside. To support this proposition we shall explore the quasi-contractual principles which enable one contracting party, the victim of a crime committed by the other party in entering the contract, to defeat this contract.In Browning v. Morris, in an oft-quoted statement by Lord Mansfield, the following principle was declared: But, where contracts or transactions are prohibited by positive statutes, for protecting one set of men from another set of men; the one, from their situation and condition, being liable to be oppressed or imposed upon by the other; there, the parties are not in pan delicto; and in furtherance of these statutes, the person injured, after the transaction is finished and completed, may bring an action and defeat the contract.

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