AMERICAN OPTIONS AND INCOMPLETE INFORMATION

2019 ◽  
Vol 22 (06) ◽  
pp. 1950035 ◽  
Author(s):  
ERIK EKSTRÖM ◽  
MARTIN VANNESTÅL
Keyword(s):  
Incomplete Information ◽  
American Options ◽  
Lower Boundary ◽  
Complete Information ◽  
Call Option ◽  
Standard Case ◽  
Underlying Process ◽  
Parameter Values ◽  
American Put

We study the optimal exercise of American options under incomplete information about the drift of the underlying process, and we show that quite unexpected phenomena may occur. In fact, certain parameter values give rise to stopping regions very different from the standard case of complete information. For example, we show that for the American put (call) option it is sometimes optimal to exercise the option when the underlying process reaches an upper (lower) boundary.

scholarly journals Spillovers and R&D Incentive under Incomplete Information

2018 ◽  
Vol 6 (1-2) ◽  
pp. 50-65 ◽  
Author(s):  
Rittwik Chatterjee ◽  
Srobonti Chattopadhyay ◽  
Tarun Kabiraj
Keyword(s):  
Distribution Function ◽  
Incomplete Information ◽  
Private Information ◽  
Complete Information ◽  
Jel Classification ◽  
General Distribution ◽  
Two Stage ◽  
Stage Game ◽  
Alternative Scenarios

Spillovers of R&D outcome affect the R&D decision of a firm. The present paper discusses the R&D incentives of a firm when the extent of R&D spillover is private information to each firm. We construct a two-stage game involving two firms when the firms first decide simultaneously whether to invest in R&D or not, then they compete in quantity. Assuming general distribution function of firm types we compare R&D incentives of firms under alternative scenarios based on different informational structures. The paper shows that while R&D spillovers reduce R&D incentives under complete information unambiguously, however, it can be larger under incomplete information. JEL Classification: D43, D82, L13, O31

scholarly journals Distance Metrics of D Numbers

2020 ◽  
Author(s):  
Liguo Fei ◽  
Yuqiang Feng
Keyword(s):  
Number Theory ◽  
Incomplete Information ◽  
Distance Function ◽  
Distance Measure ◽  
Complete Information ◽  
Belief Function ◽  
Distance Metrics ◽  
Modeling Methods ◽  
The Difference ◽  
D Numbers

Belief function has always played an indispensable role in modeling cognitive uncertainty. As an inherited version, the theory of D numbers has been proposed and developed in a more efficient and robust way. Within the framework of D number theory, two more generalized properties are extended: (1) the elements in the frame of discernment (FOD) of D numbers do not required to be mutually exclusive strictly; (2) the completeness constraint is released. The investigation shows that the distance function is very significant in measuring the difference between two D numbers, especially in information fusion and decision. Modeling methods of uncertainty that incorporate D numbers have become increasingly popular, however, very few approaches have tackled the challenges of distance metrics. In this study, the distance measure of two D numbers is presented in cases, including complete information, incomplete information, and non-exclusive elements

Incomplete Information in Multidimensional Databases

2003 ◽  
pp. 282-309 ◽  
Author(s):  
Cirtis E. Dyreson ◽  
Torben Bach Pedersen ◽  
Christian S. Jensen
Keyword(s):  
Incomplete Information ◽  
Complete Information ◽  
Multidimensional Data ◽  
Uncertain Information ◽  
Real World Data ◽  
Multidimensional Database ◽  
Simple Strategy ◽  
Multidimensional Databases ◽  
Derived Data ◽  
Base Data

While incomplete information is endemic to real-world data, current multidimensional data models are not engineered to manage incomplete information in base data, derived data, and dimensions. This chapter presents several strategies for managing incomplete information in multidimensional databases. Which strategy to use is dependent on the kind of incomplete information present, and also on where it occurs in the multidimensional database. A relatively simple strategy is to replace incomplete information with appropriate, complete information. The advantage of this strategy is that all multidimensional databases can manage complete information. Other strategies require more substantial changes to the multidimensional database. One strategy is to reflect the incompleteness in computed aggregates, which is possible only if the multidimensional database allows incomplete values in its hierarchies. Another strategy is to measure the amount of incompleteness in aggregated values by tallying how much uncertain information went into their production.

scholarly journals Sensitivity of Late-Glacial and Holocene Climates to the Combined Effects of Orbital Parameter Changes and Lower Boundary Condition Changes: “Snapshot” Simulations with A General Circulation Model for 18, 9, AND 6 ka BP

1984 ◽  
Vol 5 ◽  
pp. 85-87 ◽  
Author(s):  
John E. Kutzbach ◽  
P. J. Guetter
Keyword(s):  
Solar Radiation ◽  
Boundary Conditions ◽  
General Circulation ◽  
Ice Sheet ◽  
Lower Boundary ◽  
Circulation Model ◽  
Late Glacial ◽  
Orbital Parameter ◽  
Ocean Temperature ◽  
Parameter Values

Sensitivity experiments can be used to illustrate the response of the general circulation to prescribed changes in lower boundary conditions (such as ocean temperature) or external forcing conditions (such as solar radiation). The climatic record from the late-glacial and the Holocene provides examples for both types of prescribed change experiments. A number of general circulation model experiments have been carried out. These are reviewed.At 18 ka 8P, orbital parameter values were very much like those of today, but the lower boundary conditions (ocean temperature, ice-sheet extent, etc.) were very different. The change in ocean temperature, and ice-sheet extent and thickness, were prescribed from the results of the Climate: Long-range Investigation Mapping and Prediction (CLIMAP) project.At 9 ka BP, orbital parameter values were very different from present, leading to increased radiation in July and decreased radiation in January (compared to present). The North American ice sheet still covered a significant area, so that lower boundary conditions also differed from the present ones. The combined and individual effects of these prescribed changes on the general circulation are reviewed, particularly in the context of changes of the monsoon circulation.At 6 ka BP, the solar radiation distribution differed from that of today in much the same fashion as at 9 ka BP, although the magnitude of the change was reduced. Lower boundary conditions were probably very similar to those of today.A series of experimental results from 18, 9, and 6 ka BP are presented as “snapshot” estimates of the paleoclimate of those times. The results are based upon simulations with the community climate model of the National Center for Atmospheric Research.

THE EARLY EXERCISE PREMIUM IN AMERICAN OPTIONS BY USING NONPARAMETRIC REGRESSIONS

2018 ◽  
Vol 21 (07) ◽  
pp. 1850039
Author(s):  
WEIPING LI ◽  
SU CHEN
Keyword(s):  
Mean Square Error ◽  
Nonparametric Regression ◽  
American Options ◽  
Mean Square ◽  
Early Exercise ◽  
American Put Option ◽  
Put Option ◽  
Out Of Sample ◽  
American Put ◽  
Early Exercise Premium

The early exercise premium and the price of an American put option are evaluated by using nonparametric regression on the time to expiration, the moneyness and the volatility of underlying assets. In terms of mean square error (MSE), our nonparametric methods of American put option pricings outperform the existing classical methods for both in-the-sample (1 September 2011–31 January 2012) and out-of-sample (1 September 2012–28 February 2013) testings on the S&P 100 Index (OEX). Our methods have better predictions and more accurate approximations. The Greek letters for both the early exercise premium and the American put option are computed numerically.

scholarly journals ROBUST HETEROCLINIC CYCLES IN TWO-DIMENSIONAL RAYLEIGH–BÉNARD CONVECTION WITHOUT BOUSSINESQ SYMMETRY

2002 ◽  
Vol 12 (11) ◽  
pp. 2501-2522 ◽  
Author(s):  
ISABEL MERCADER ◽  
JOANA PRAT ◽  
EDGAR KNOBLOCH
Keyword(s):  
Rayleigh Number ◽  
Lower Boundary ◽  
Two Dimensions ◽  
External Parameter ◽  
Onset Of Convection ◽  
Current Dissipation ◽  
Parameter Values ◽  
Rayleigh Benard Convection ◽  
Spatial Resonance ◽  
Rayleigh Benard

The onset of convection in systems that are heated via current dissipation in the lower boundary or that lose heat from the top boundary via Newton's law of cooling is formulated as a bifurcation problem. The Rayleigh number as usually defined is shown to be inappropriate as a bifurcation parameter since the temperature difference across the layer depends on the amplitude of convection and hence changes as convection evolves at fixed external parameter values. A modified Rayleigh number is introduced that does remain constant even when the system is evolving, and solutions obtained with the standard formulation are compared with those obtained via the new one. Near the 1 : 2 spatial resonance in low Prandtl number fluids these effects open up intervals of Rayleigh number with no stable solutions in the form of steady convection or steadily traveling waves. Direct numerical simulations in two dimensions show that in such intervals the dynamics typically take the form of a nearly heteroclinic modulated traveling wave. This wave may be quasiperiodic or chaotic.

Optimal Controls for a Single Species Fishery and the Economic Value of Research

1976 ◽  
Vol 33 (4) ◽  
pp. 793-809 ◽  
Author(s):  
C. C. Huang ◽  
Ilan B. Vertinsky ◽  
Norman J. Wilimovsky
Keyword(s):  
Optimal Allocation ◽  
Probability Distributions ◽  
Economic Value ◽  
Mesh Size ◽  
Single Species ◽  
Complete Information ◽  
Optimal Controls ◽  
Optimal Policies ◽  
Solution Methods ◽  
Parameter Values

Mathematical proofs and analyses of solution methods are presented for determining optimal policies for the management of a single species fishery under equilibrium conditions. Previous intuitive arguments for solution of optimal policies controlling mesh size and fishing rate given complete information are explicitly proven. The analysis is extended to the case where some of the parameters describing the dynamics of the population are known only imprecisely to the manager. Using probability distributions for those unknown parameter values the problem is cast as a stochastic program where expected sustained net revenues from the fishery are maximized. The associated problem of optimal allocation of research resources under uncertainty conditions is considered by evaluating the direct value of such information to management activities.Examples and algorithms are presented for the class of problems discussed.

scholarly journals Approximate ordinary differential equations for the optimal exercise boundaries of American put and call options

2013 ◽  
Vol 25 (1) ◽  
pp. 27-43 ◽  
Author(s):  
MARIANITO R. RODRIGO
Keyword(s):  
Differential Equations ◽  
Fluid Mechanics ◽  
Numerical Simulations ◽  
Ordinary Differential Equations ◽  
Boundary Layers ◽  
Mellin Transform ◽  
Call Option ◽  
Option Prices ◽  
Analytical Formulas ◽  
American Put

We revisit the American put and call option valuation problems. We derive analytical formulas for the option prices and approximate ordinary differential equations for the optimal exercise boundaries. Numerical simulations yield accurate option prices and comparable computational speeds when benchmarked against the binomial method for calculating option prices. Our approach is based on the Mellin transform and an adaptation of the Kármán–Pohlausen technique for boundary layers in fluid mechanics.

Pre-contest Communication Incentives

2017 ◽  
Vol 18 (1) ◽  
Author(s):  
Mustafa Yildirim
Keyword(s):  
Incomplete Information ◽  
Complete Information ◽  
Psychological Strength

AbstractTo demonstrate resolution and psychological strength, players often engage in pre-contest communication by publicly stating their desire to win an upcoming contest. Existing explanations for this phenomenon revolve around incomplete information and signaling. In this paper, I offer a complementary explanation that does not rely on signaling. Within a complete information setup, I show that players may have an incentive for pre-contest communication if, in addition to an audience (reputational) cost when the statement does not materialize, the players also incur an audience reward (credibility gain) when the statement materializes.

Game Theory and Other Modeling Approaches

2018 ◽  
Author(s):  
Frank C. Zagare ◽  
Branislav L. Slantchev
Keyword(s):  
Game Theory ◽  
International Relations ◽  
Incomplete Information ◽  
Dynamic Games ◽  
Complete Information ◽  
Third Wave ◽  
Extensive Form ◽  
Interactive Decision Making ◽  
The Game Theory ◽  
Almost All

Game theory is the science of interactive decision making. It has been used in the field of international relations (IR) for over 50 years. Almost all of the early applications of game theory in international relations drew upon the theory of zero-sum games, but the first generation of applications was also developed during the most intense period of the Cold War. The theoretical foundations for the second wave of the game theory literature in international relations were laid by a mathematician, John Nash, a co-recipient of the 1994 Nobel Prize in economics. His major achievement was to generalize the minimax solution which emerged from the first wave. The result is the now famous Nash equilibrium—the accepted measure of rational behavior in strategic form games. During the third wave, from roughly the early to mid-1980s to the mid-1990s, there was a distinct move away from static strategic form games toward dynamic games depicted in extensive form. The assumption of complete information also fell by the wayside; games of incomplete information became the norm. Technical refinements of Nash’s equilibrium concept both encouraged and facilitated these important developments. In the fourth and final wave, which can be dated, roughly, from around the middle of the 1990s, extensive form games of incomplete information appeared regularly in the strategic literature. The fourth wave is a period in which game theory was no longer considered a niche methodology, having finally emerged as a mainstream theoretical tool.

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