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We study the pricing and the hedging of claim {\psi} which depends on the default times of two firms A and B. In fact, we assume that, in the market, we can not buy or sell any defaultable bond of the firm B but we can only trade…
This paper presents an axiomatic approach to finite Markov decision processes where the discount rate is zero. One of the principal difficulties in the no discounting case is that, even if attention is restricted to stationary policies, a…
The proposed model modifies option pricing formulas for the basic case of log-normal probability distribution providing correspondence to formulated criteria of efficiency and completeness. The model is self-calibrating by historic…
Euclidean Markov decision processes are a powerful tool for modeling control problems under uncertainty over continuous domains. Finite state imprecise, Markov decision processes can be used to approximate the behavior of these infinite…
In this paper, we consider risk-sensitive Markov Decision Processes (MDPs) with Borel state and action spaces and unbounded cost under both finite and infinite planning horizons. Our optimality criterion is based on the recursive…
We propose a model which can be jointly calibrated to the corporate bond term structure and equity option volatility surface of the same company. Our purpose is to obtain explicit bond and equity option pricing formulas that can be…
Markov automata combine non-determinism, probabilistic branching, and exponentially distributed delays. This compositional variant of continuous-time Markov decision processes is used in reliability engineering, performance evaluation and…
This note provides upper bounds on the number of operations required to compute by value iterations a nearly optimal policy for an infinite-horizon discounted Markov decision process with a finite number of states and actions. For a given…
In this paper, we give a numerical method for pricing long maturity, path dependent options by using the Markov property for each underlying asset. This enables us to approximate a path dependent option by using some kinds of plain…
We introduce the use of reinforcement learning for indirect mechanisms, working with the existing class of sequential price mechanisms, which generalizes both serial dictatorship and posted price mechanisms and essentially characterizes all…
The online Markov decision process (MDP) is a generalization of the classical Markov decision process that incorporates changing reward functions. In this paper, we propose practical online MDP algorithms with policy iteration and…
We develop a finite horizon continuous time market model, where risk averse investors maximize utility from terminal wealth by dynamically investing in a risk-free money market account, a stock written on a default-free dividend process,…
Spot option prices, forwards and options on forwards relevant for the commodity markets are computed when the underlying process S is modelled as an exponential of a process {\xi} with memory as e.g. a L\'evy semi-stationary process.…
Generating realistic synthetic option prices requires implied volatility as an input, yet implied volatility is itself derived from observed option prices, creating a circular dependency that limits synthetic data for machine-learning and…
Markov decision processes (MDPs) are the defacto frame-work for sequential decision making in the presence ofstochastic uncertainty. A classical optimization criterion forMDPs is to maximize the expected discounted-sum pay-off, which…
We consider the pricing of derivatives written on accumulated marks, such as weather derivatives or aggregate loss claims, using a self-exciting marked point process. The jump intensity mean-reverts between events and increases at jump…
We formalize the problem of maximizing the mean-payoff value with high probability while satisfying a parity objective in a Markov decision process (MDP) with unknown probabilistic transition function and unknown reward function. Assuming…
This paper investigates the optimization problem of an infinite stage discrete time Markov decision process (MDP) with a long-run average metric considering both mean and variance of rewards together. Such performance metric is important…
In recent years, quantitative investment methods combined with artificial intelligence have attracted more and more attention from investors and researchers. Existing related methods based on the supervised learning are not very suitable…
We consider a piecewise deterministic Markov decision process, where the expected exponential utility of total (nonnegative) cost is to be minimized. The cost rate, transition rate and post-jump distributions are under control. The state…