scholarly journals Market stability switches in a continuous-time financial market with heterogeneous beliefs

2009 ◽  
Vol 26 (6) ◽  
pp. 1432-1442 ◽  
Author(s):  
Xue-Zhong He ◽  
Kai Li ◽  
Junjie Wei ◽  
Min Zheng
Keyword(s):  
Financial Market ◽  
Continuous Time ◽  
Heterogeneous Beliefs ◽  
Stability Switches ◽  
Market Stability

scholarly journals Ruin Probabilities in a Finite-Horizon Risk Model with Investment and Reinsurance

2012 ◽  
Vol 49 (04) ◽  
pp. 954-966
Author(s):  
R. Romera ◽  
W. Runggaldier
Keyword(s):  
Financial Market ◽  
Continuous Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Finite Horizon ◽  
Ruin Probabilities ◽  
Optimal Solutions ◽  
Semi Markov Process ◽  
Insurance Model ◽  
Recursive Relations

A finite-horizon insurance model is studied where the risk/reserve process can be controlled by reinsurance and investment in the financial market. Our setting is innovative in the sense that we describe in a unified way the timing of the events, that is, the arrivals of claims and the changes of the prices in the financial market, by means of a continuous-time semi-Markov process which appears to be more realistic than, say, classical diffusion-based models. Obtaining explicit optimal solutions for the minimizing ruin probability is a difficult task. Therefore we derive a specific methodology, based on recursive relations for the ruin probability, to obtain a reinsurance and investment policy that minimizes an exponential bound (Lundberg-type bound) on the ruin probability.

HEDGING OPTIONS IN A DOUBLY MARKOV-MODULATED FINANCIAL MARKET VIA STOCHASTIC FLOWS

2019 ◽  
Vol 22 (08) ◽  
pp. 1950047 ◽  
Author(s):  
TAK KUEN SIU ◽  
ROBERT J. ELLIOTT
Keyword(s):  
Markov Chain ◽  
Financial Market ◽  
Continuous Time ◽  
Regime Switching ◽  
Stochastic Flows ◽  
Finite State ◽  
Markov Modulated ◽  
Appreciation Rate ◽  
The Interest Rate ◽  
Over Time

The hedging of a European-style contingent claim is studied in a continuous-time doubly Markov-modulated financial market, where the interest rate of a bond is modulated by an observable, continuous-time, finite-state, Markov chain and the appreciation rate of a risky share is modulated by a continuous-time, finite-state, hidden Markov chain. The first chain describes the evolution of credit ratings of the bond over time while the second chain models the evolution of the hidden state of an underlying economy over time. Stochastic flows of diffeomorphisms are used to derive some hedge quantities, or Greeks, for the claim. A mixed filter-based and regime-switching Black–Scholes partial differential equation is obtained governing the price of the claim. It will be shown that the delta hedge ratio process obtained from stochastic flows is a risk-minimizing, admissible mean-self-financing portfolio process. Both the first-order and second-order Greeks will be considered.

scholarly journals Ruin Probabilities in a Finite-Horizon Risk Model with Investment and Reinsurance

2012 ◽  
Vol 49 (4) ◽  
pp. 954-966 ◽  
Author(s):  
R. Romera ◽  
W. Runggaldier
Keyword(s):  
Financial Market ◽  
Continuous Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Finite Horizon ◽  
Ruin Probabilities ◽  
Optimal Solutions ◽  
Semi Markov Process ◽  
Insurance Model ◽  
Recursive Relations

A finite-horizon insurance model is studied where the risk/reserve process can be controlled by reinsurance and investment in the financial market. Our setting is innovative in the sense that we describe in a unified way the timing of the events, that is, the arrivals of claims and the changes of the prices in the financial market, by means of a continuous-time semi-Markov process which appears to be more realistic than, say, classical diffusion-based models. Obtaining explicit optimal solutions for the minimizing ruin probability is a difficult task. Therefore we derive a specific methodology, based on recursive relations for the ruin probability, to obtain a reinsurance and investment policy that minimizes an exponential bound (Lundberg-type bound) on the ruin probability.

scholarly journals Integration by Parts and Martingale Representation for a Markov Chain

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Tak Kuen Siu
Keyword(s):  
Markov Chain ◽  
Financial Market ◽  
Continuous Time ◽  
Contingent Claims ◽  
Jump Processes ◽  
Stochastic Integrals ◽  
Integration By Parts ◽  
Martingale Representation ◽  
Finite State ◽  
Change Of Measures

Integration-by-parts formulas for functions of fundamental jump processes relating to a continuous-time, finite-state Markov chain are derived using Bismut's change of measures approach to Malliavin calculus. New expressions for the integrands in stochastic integrals corresponding to representations of martingales for the fundamental jump processes are derived using the integration-by-parts formulas. These results are then applied to hedge contingent claims in a Markov chain financial market, which provides a practical motivation for the developments of the integration-by-parts formulas and the martingale representations.

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.

scholarly journals TRANSACTION COSTS INFLUENCE ON THE STABILITY OF FINANCIAL MARKET: AGENT-BASED SIMULATION

2013 ◽  
Vol 14 (Supplement_1) ◽  
pp. S1-S12 ◽  
Author(s):  
Roman Šperka ◽  
Marek Spišák
Keyword(s):  
Transaction Costs ◽  
Financial Market ◽  
Positive Impact ◽  
State Theory ◽  
Market Model ◽  
Agent Based Simulation ◽  
Trading Rules ◽  
Agent Based ◽  
Market Stability ◽  
Financial Market Stability

We implement an agent-based simulation of financial market model. Agent-based simulations are used nowadays as an alternative to the traditional models, based on predetermined equilibrium state theory. Agent technology brings some kind of local intelligence and rational expectations to the decision support system of financial market participants. Agents follow technical and fundamental trading rules to determine their speculative investment positions. We consider direct interactions between speculators and they may decide to change their trading behaviour. If a technical trader meets a fundamental trader and they realize that fundamental trading has been more profitable than technical trading in recent past, the probability that the technical trader switches to the fundamental trading rules is relatively high. In particular the influence of transaction costs is studied in this paper. Transaction costs can be increased by the off-market regulation (for example in the form of taxes) on financial market stability, by overall volume of trade and other market characteristics. The paper shows a positive impact of suitable transaction costs on the financial market stability in the long run.

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