Incomplete markets: convergence of options values under the minimal martingale measure

1999 ◽  
Vol 31 (04) ◽  
pp. 1058-1077 ◽  
Author(s):  
Jean-Luc Prigent
Keyword(s):  
Financial Market ◽  
Incomplete Markets ◽  
Stock Prices ◽  
Continuous Time ◽  
Martingale Measure ◽  
Minimal Martingale Measure ◽  
Mild Assumption ◽  
The Stability ◽  
Minimal Measure ◽  
Nikodym Derivative

In the setting of incomplete markets, this paper presents a general result of convergence for derivative assets prices. It is proved that the minimal martingale measure first introduced by Föllmer and Schweizer is a convenient tool for the stability under convergence. This extends previous well-known results when the markets are complete both in discrete time and continuous time. Taking into account the structure of stock prices, a mild assumption is made. It implies the joint convergence of the sequences of stock prices and of the Radon-Nikodym derivative of the minimal measure. The convergence of the derivatives prices follows.This property is illustrated in the main classes of financial market models.

Incomplete markets: convergence of options values under the minimal martingale measure

1999 ◽  
Vol 31 (4) ◽  
pp. 1058-1077 ◽  
Author(s):  
Jean-Luc Prigent
Keyword(s):  
Financial Market ◽  
Incomplete Markets ◽  
Stock Prices ◽  
Continuous Time ◽  
Martingale Measure ◽  
Minimal Martingale Measure ◽  
Mild Assumption ◽  
The Stability ◽  
Minimal Measure ◽  
Nikodym Derivative

In the setting of incomplete markets, this paper presents a general result of convergence for derivative assets prices. It is proved that the minimal martingale measure first introduced by Föllmer and Schweizer is a convenient tool for the stability under convergence. This extends previous well-known results when the markets are complete both in discrete time and continuous time. Taking into account the structure of stock prices, a mild assumption is made. It implies the joint convergence of the sequences of stock prices and of the Radon-Nikodym derivative of the minimal measure. The convergence of the derivatives prices follows.This property is illustrated in the main classes of financial market models.

Arbitrage Theory in Continuous Time

2019 ◽  
Author(s):  
Tomas Björk
Keyword(s):  
Incomplete Markets ◽  
Continuous Time ◽  
Dynamic Equilibrium ◽  
Factor Model ◽  
Good Deal ◽  
Financial Derivatives ◽  
Equilibrium Theory ◽  
Martingale Measure ◽  
Fourth Edition ◽  
Optimal Stopping Theory

The fourth edition of this textbook on pricing and hedging of financial derivatives, now also including dynamic equilibrium theory, continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous time arbitrage pricing of financial derivatives, including stochastic optimal control theory and optimal stopping theory, the book is designed for graduate students in economics and mathematics, and combines the necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter. All concepts and ideas are discussed, not only from a mathematics point of view, but the mathematical theory is also always supplemented with lots of intuitive economic arguments. In the substantially extended fourth edition Tomas Björk has added completely new chapters on incomplete markets, treating such topics as the Esscher transform, the minimal martingale measure, f-divergences, optimal investment theory for incomplete markets, and good deal bounds. There is also an entirely new part of the book presenting dynamic equilibrium theory. This includes several chapters on unit net supply endowments models, and the Cox–Ingersoll–Ross equilibrium factor model (including the CIR equilibrium interest rate model). Providing two full treatments of arbitrage theory—the classical delta hedging approach and the modern martingale approach—the book is written in such a way that these approaches can be studied independently of each other, thus providing the less mathematically oriented reader with a self-contained introduction to arbitrage theory and equilibrium theory, while at the same time allowing the more advanced student to see the full theory in action.

A SHOT NOISE MODEL FOR FINANCIAL ASSETS

2008 ◽  
Vol 11 (01) ◽  
pp. 87-106 ◽  
Author(s):  
TIMO ALTMANN ◽  
THORSTEN SCHMIDT ◽  
WINFRIED STUTE
Keyword(s):  
Simulation Study ◽  
Shot Noise ◽  
Stock Prices ◽  
Continuous Time ◽  
Noise Model ◽  
Martingale Measure ◽  
Financial Assets ◽  
Hedging Strategy ◽  
Noise Effects ◽  
Abrupt Changes

In this article we propose and study a model for stock prices which allows for shot-noise effects. This means that abrupt changes caused by jumps may fade away as time goes by. This model is incomplete. We derive the minimal martingale measure in discrete and continuous time and discuss the associated hedging strategy. Finally, a simulation study is included to show that our model is able to produce smile effects.

Stability of real-time hybrid simulation involving time-varying delay and direct integration algorithms

2021 ◽  
pp. 107754632110016
Author(s):  
Liang Huang ◽  
Cheng Chen ◽  
Shenjiang Huang ◽  
Jingfeng Wang
Keyword(s):  
Real Time ◽  
Discrete Time ◽  
Continuous Time ◽  
Hybrid Simulation ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Integration Algorithms ◽  
The Stability ◽  
Continuous Time System

Stability presents a critical issue for real-time hybrid simulation. Actuator delay might destabilize the real-time test without proper compensation. Previous research often assumed real-time hybrid simulation as a continuous-time system; however, it is more appropriately treated as a discrete-time system because of application of digital devices and integration algorithms. By using the Lyapunov–Krasovskii theory, this study explores the convoluted effect of integration algorithms and actuator delay on the stability of real-time hybrid simulation. Both theoretical and numerical analysis results demonstrate that (1) the direct integration algorithm is preferably used for real-time hybrid simulation because of its computational efficiency; (2) the stability analysis of real-time hybrid simulation highly depends on actuator delay models, and the actuator model that accounts for time-varying characteristic will lead to more conservative stability; and (3) the integration step is constrained by the algorithm and structural frequencies. Moreover, when the step is small, the stability of the discrete-time system will approach that of the corresponding continuous-time system. The study establishes a bridge between continuous- and discrete-time systems for stability analysis of real-time hybrid simulation.

Densities of scaling limits of coupled continuous time random walks

2016 ◽  
Vol 19 (6) ◽  
Author(s):  
Marcin Magdziarz ◽  
Tomasz Zorawik
Keyword(s):  
Fractional Differential Equations ◽  
Continuous Time ◽  
Stability Index ◽  
Scaling Limits ◽  
Explicit Formulas ◽  
Material Derivative ◽  
Lévy Walks ◽  
Continuous Time Random Walks ◽  
Fractional Differential ◽  
The Stability

AbstractIn this paper we derive explicit formulas for the densities of Lévy walks. Our results cover both jump-first and wait-first scenarios. The obtained densities solve certain fractional differential equations involving fractional material derivative operators. In the particular case, when the stability index is rational, the densities can be represented as an integral of Meijer

PSYCHOLOGICAL ASPECTS OF ORGANIZATION OF FRAUD SCHEMES IN THE FIELD OF THE FINANCIAL MARKET

2021 ◽  
Vol 1 (12) ◽  
pp. 69-77
Author(s):  
Аleksey V. Zverev ◽  
◽  
Marina Yu. Mishina ◽  
Andrey V. Novikov ◽  
◽  
...  
Keyword(s):  
Critical Thinking ◽  
Financial Market ◽  
Financial Services ◽  
Psychological Aspects ◽  
Financial Fraud ◽  
Stressful Situation ◽  
Potential Victim ◽  
The Stability ◽  
The Relationship

This article reflects the peculiarities of the psychological connection between a financial fraudster and his potential victim. The process of forming a stressful situation depending on the type of financial fraud is described, the reasons for its occurrence and the result of implementation associated with a decrease in critical thinking are indicated. The essence is also revealed, including from the perspective of the relationship between the fraudster and the potential victim, and the types of financial fraud and practical examples of their manifestation are considered. The psychological portrait of a financial fraudster and his transformation in connection with the changing preferences of consumers of financial services are described. The role of the Bank of Russia in reducing the activity of financial fraud and ensuring the stability of the financial market is reflected.

Consensus Problem of Singular Multi-Agent Systems with Continuous-Time and Fixed Topology

2013 ◽  
Vol 278-280 ◽  
pp. 1687-1691
Author(s):  
Tong Qiang Jiang ◽  
Jia Wei He ◽  
Yan Ping Gao
Keyword(s):  
Continuous Time ◽  
Spanning Tree ◽  
Undirected Graph ◽  
Necessary Condition ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent ◽  
Fixed Topology ◽  
The Stability ◽  
Sufficient And Necessary Condition

The consensus problems of two situations for singular multi-agent systems with fixed topology are discussed: directed graph without spanning tree and the disconnected undirected graph. A sufficient and necessary condition is obtained by applying the stability theory and the system is reachable asymptotically. But for normal systems, this can’t occur in upper two situations. Finally a simulation example is provided to verify the effectiveness of our theoretical result.

scholarly journals Understanding the Interdependency between the Nifty 50 Future Index and the Advanced Future Stock Market through Econometrics

2019 ◽  
Vol 8 (4) ◽  
pp. 3660-3664
Keyword(s):  
Hong Kong ◽  
Stock Market ◽  
Granger Causality ◽  
Foreign Exchange ◽  
Financial Market ◽  
Stock Prices ◽  
Economic Condition ◽  
The Future ◽  
Bidirectional Movement ◽  
High Degree

In recent times the stock market is accepted as a tool to measure the economic condition of a nation. It is found that the Indian financial market as highly volatile due to the lower value of rupees in foreign exchange with the dollar. This motivated the researchers to measure the interdependencies of [Nifty 50 future (India), Nikkei 225(Japan), NASDAQ 100 Futures (USA), Dow Jones 30 (USA), SSEC (China), Hang Seng Future (Hong Kong), and FTSE 100 (London)]. The analysis covers monthly stock prices for a period of 10years from April 2008 to March 2018. The measurement of interdependencies is studied through granger causality and correlation after the confirmation of the non-normality of data and stationary of data. The result shows a high degree of correlation between NASDAQ and Dow Jones shows 98.76% followed by 96.89% between Nifty 50 future and NASDAQ. The co-movement result of Nifty 50 future through granger causality states Nifty 50 future can explain the future stock market of Nikkei (Japan) and SSEC (China) and the Hang Seng future (Hong Kong) has a bidirectional movement with Nifty 50 futures. The study is useful for the investors to identify the interdependencies of the indices and understand the movement in a significant manner.

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