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This chapter presents a review of the dividend discount models starting from the basic models (Williams 1938, Gordon and Shapiro 1956) to more recent and complex models (Ghezzi and Piccardi 2003, Barbu et al. 2017, D'Amico and De Blasis…
Avanzi et al. (2016) recently studied an optimal dividend problem where dividends are paid both periodically and continuously with different transaction costs. In the Brownian model with Poissonian periodic dividend payment opportunities,…
We study a linear price impact model including other liquidity takers, whose flow of orders either follows a Poisson or a Hawkes process. The optimal execution problem is solved explicitly in this context, and the closed-formula optimal…
This paper is devoted to invest an optimal investment strategy for a defined-contribution (DC) pension plan under the Ornstein-Uhlenbeck (O-U) process and the loan. By considering risk-free asset, a risky asset driven by O-U process and a…
We study a De Finetti's optimal dividend and capital injection problem under a Markov additive model. The surplus process without dividend and capital injection is assumed to follow a spectrally positive Markov additive process (MAP).…
We develop a non-parametric, semimartingale optimal transport, calibration methodology for local volatility models with stochastic interest rate. The method finds a fully calibrated model which is the closest, in a way that can be defined…
This study investigates an optimal investment problem for an insurance company operating under the Cramer-Lundberg risk model, where investments are made in both a risky asset and a risk-free asset. In contrast to other literature that…
We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer's surplus is governed…
In this paper we solve the dividend optimization problem for a corporation or a financial institution when the managers of the corporation are facing (regulatory) implementation delays. We consider several cash reservoir models for the firm…
The Vlasov-Fokker-Planck equation describes the evolution of the probability density of the position and velocity of particles under the influence of external confinement, interaction, friction, and stochastic force. It is well-known that…
In this paper, an optimization problem for the monotone mean-variance(MMV) criterion is considered in the perspective of the insurance company. The MMV criterion is an amended version of the classical mean-variance(MV) criterion which…
This analysis derives the maximum likelihood estimator and applies Bayesian inference to model geometric Brownian motion, incorporating jump diffusion to account for sudden market shifts. The Bayesian approach is implemented using Markov…
In this work we study the optimal execution problem with multiplicative price impact in algorithm trading, when an agent holds an initial position of shares of a financial asset. The inter-selling-decision times are modelled by the arrival…
We investigate the problem of optimal dividend distribution for a company in the presence of regime shifts. We consider a company whose cumulative net revenues evolve as a Brownian motion with positive drift that is modulated by a finite…
We introduce a price impact model which accounts for finite market depth, tightness and resilience. Its coupled bid- and ask-price dynamics induce convex liquidity costs. We provide existence of an optimal solution to the classical problem…
This paper studies a {\it reversible} investment problem where a social planner aims to control its capacity production in order to fit optimally the random demand of a good. Our model allows for general diffusion dynamics on the demand as…
In this paper we propose a new way of proving the value of a firm that is currently producing a certain product and faces the option to exit the market. The problem of optimal exiting is an optimal stopping problem, that can be solved using…
We study a stochastic optimal control problem for a partially observed diffusion. By using the control randomization method in [4], we prove a corresponding randomized dynamic programming principle (DPP) for the value function, which is…
We consider a stock that follows a geometric Brownian motion (GBM) and a riskless asset continuously compounded at a constant rate. We assume that the stock can go bankrupt, i.e., lose all of its value, at some exogenous random time…
In this paper we propose a new model for pricing stock and dividend derivatives. We jointly specify dynamics for the stock price and the dividend rate such that the stock price is positive and the dividend rate non-negative. In its simplest…