1,720,979 research outputs found
Classical solutions of the backward PIDE for Markov modulated marked point processes and applications to CAT bonds
No full textThe objective of this paper is to give conditions ensuring that the backward partial integro differential equation associated with a multidimensional jump-diffusion with a pure jump component has a unique classical solution; that is the solution is continuous, twice differentiable in the diffusion component and differentiable in time. Our proof uses a probabilistic argument and extends the results of Pham (1998) to processes with a pure jump component where the jump intensity is modulated by a diffusion process. This result is particularly useful in some applications to pricing and hedging of financial and actuarial instruments, and we provide an example to pricing of CAT bonds. (C) 2021 Elsevier B.V. All rights reserved
Stochastic filtering of a pure jump process with predictable jumps and path-dependent local characteristics
Full text linkThe objective of this paper is to study the filtering problem for a system of partially observable processes (X, Y), where X is a non-Markovian pure jump process representing the signal and Y is a general jump diffusion which provides observations. Our model covers the case where both processes are not necessarily quasi left-continuous, allowing them to jump at predictable stopping times. By introducing the Markovian version of the signal, we are able to compute an explicit equation for the filter via the innovations approach
The value of knowing the market price of risk
No full textWe study an optimal allocation problem in a financial market with one risk-free and one risky asset, when the market is driven by a stochastic market price of risk. The problem is set in continuous time, for an investor with a constant relative risk aversion utility, under two scenarios: when the market price of risk is observable (the full information case), and when it is not (the partial information case). The corresponding market models are complete in the partial information case and incomplete under full information. We study how the access to more accurate information on the market price of risk affects the optimal strategies and we determine the maximum price that the investor would be willing to pay to receive such information. In particular, we examine two cases of additional information, when an exact observation of the market price of risk is available either at time 0 only (the initial information case), or during the whole investment period (the dynamic information case)
Optimal investment and proportional reinsurance in a regime-switching market model under forward preferences
Full text linkIn this paper, we study the optimal investment and reinsurance problem of an insurance company whose investment preferences are described via a forward dynamic exponential utility in a regime-switching market model. Financial and actuarial frameworks are dependent since stock prices and insurance claims vary according to a common factor given by a continuous time finite state Markov chain. We construct the value function and we prove that it is a forward dynamic utility. Then, we characterize the optimal investment strategy and the optimal proportional level of reinsurance. We also perform numerical experiments and provide sensitivity analyses with respect to some model parameters
Unit-linked life insurance policies: Optimal hedging in partially observable market models
No full textIn this paper we investigate the hedging problem of a unit-linked life insurance contract via the local risk-minimization approach, when the insurer has a restricted information on the market. In particular, we consider an endowment insurance contract, that is a combination of a term insurance policy and a pure endowment, whose final value depends on the trend of a stock market where the premia the policyholder pays are invested. To allow for mutual dependence between the financial and the insurance markets, we use the progressive enlargement of filtration approach. We assume that the stock price process dynamics depends on an exogenous unobservable stochastic factor that also influences the mortality rate of the policyholder. We characterize the optimal hedging strategy in terms of the integrand in the Galtchouk Kunita Watanabe decomposition of the insurance claim with respect to the minimal martingale measure and the available information flow. We provide an explicit formula by means of predictable projection of the corresponding hedging strategy under full information with respect to the natural filtration of the risky asset price and the minimal martingale measure. Finally, we discuss applications in a Markovian setting via filtering. (C) 2017 Elsevier B.V. All rights reserved
Optimal reinsurance and investment under common shock dependence between financial and actuarial markets
No full textWe study optimal proportional reinsurance and investment strategies for an insurance company which
experiences both ordinary and catastrophic claims and wishes to maximize the expected exponential
utility of its terminal wealth. We propose a modeling setting where the insurance framework is affected
by environmental factors, and aggregate claims and stock prices are subject to common shocks, i.e. drastic
events such as earthquakes, extreme weather conditions, or even pandemics, that have an immediate
impact on the financial market and simultaneously induce insurance claims. Using a classical stochastic
control approach based on the Hamilton-Jacobi-Bellman equation, we provide a verification result for the
value function via classical solutions of two backward partial differential equations and characterize the
optimal reinsurance and investment strategy. Finally, we provide a comparison analysis to discuss the
effect of common shock dependenc
Optimal convergence trading with unobservable pricing errors
No full textWe study a dynamic portfolio optimization problem related to convergence trading, which is an investment strategy that exploits temporary mispricing by simultaneously buying relatively underpriced assets and selling short relatively overpriced ones with the expectation that their prices converge in the future. We build on the model of Liu and Timmermann (Rev Financ Stud 26(4):1048-1086, 2013) and extend it by incorporating unobservable Markov-modulated pricing errors into the price dynamics of two co-integrated assets. We characterize the optimal portfolio strategies in full and partial information settings under the assumption of unrestricted and beta-neutral strategies. By using the innovations approach, we provide the filtering equation which is essential for solving the optimization problem under partial information. Finally, in order to illustrate the model capabilities, we provide an example with a two-state Markov chain
The Föllmer–Schweizer decomposition under incomplete information
No full textIn this paper we study the Follmer-Schweizer decomposition of a square integrable random variable with respect to a given semimartingale S under restricted information. Thanks to the relationship between this decomposition and that of the projection of with respect to the given information flow, we characterize the integrand appearing in the Follmer-Schweizer decomposition under partial information in the general case where is not necessarily adapted to the available information level. For partially observable Markovian models where the dynamics of S depends on an unobservable stochastic factor X, we show how to compute the decomposition by means of filtering problems involving functions defined on an infinite-dimensional space. Moreover, in the case of a partially observed jump-diffusion model where X is described by a pure jump process taking values in a finite dimensional space, we compute explicitly the integrand in the Follmer-Schweizer decomposition by working with finite dimensional filters. Finally, we use our achievements in a financial application where we compute the optimal hedging strategy under restricted information for a European put option and provide a comparison with that under complete information
The value of information for optimal portfolio management
No full textWe study the value of information for a manager who invests in a stock market to optimize the utility of her future wealth. We consider an incomplete financial market model with a mean reverting market price of risk that cannot be directly observed by the manager. The available information is represented by the filtration generated by the stock price process. We solve the classical Merton problem for an incomplete market under partial information by means of filtering techniques and the martingale approach
Implicit incentives for fund managers with partial information
Full text linkWe study the optimal asset allocation problem for a fund manager whose compensation depends on the performance of her portfolio with respect to a benchmark. The objective of the manager is to maximise the expected utility of her final wealth. The manager observes the prices but not the values of the market price of risk that drives the expected returns. Estimates of the market price of risk get more precise as more observations are available. We formulate the problem as an optimization under partial information. The particular structure of the incentives makes the objective function not concave. Therefore, we solve the problem by combining the martingale method and a concavification procedure and we obtain the optimal wealth and the investment strategy. A numerical example shows the effect of learning on the optimal strategy
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