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We propose a model for the joint evolution of European inflation, the European Central Bank official interest rate and the short-term interest rate, in a stochastic, continuous time setting. We derive the valuation equation for a contingent…

A Discrete Boltzmann Model(DBM) based on the Shakhov model for detonation is proposed. Compared with the DBM based on the Bhatnagar-Gross-Krook (BGK) model, the current model has a flexible Prandtl numbers and consequently can be applied to…

We present Zero-Direction Probing (ZDP), a theory-only framework for detecting model drift from null directions of transformer activations without task labels or output evaluations. Under assumptions A1--A6, we prove: (i) the Variance--Leak…

We introduce a class of models for multidimensional control problems which we call skip-free Markov decision processes on trees. We describe and analyse an algorithm applicable to Markov decision processes of this type that are skip-free in…

Valuing corporate bonds in systemic economies is challenging due to intricate webs of inter-institutional exposures. When a bank defaults, cascading losses propagate through the network, with payments determined by a system of fixed-point…

The comparative statics of the optimal portfolios across individuals is carried out for a continuous-time complete market model, where the risky assets price process follows a joint geometric Brownian motion with time-dependent and…

This technical report describes a dynamic causal model of the spread of coronavirus through a population. The model is based upon ensemble or population dynamics that generate outcomes, like new cases and deaths over time. The purpose of…

We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model was already described in the literature. We present a new approach to the problem, based on partial…

We analyze a three-dimensional Keen--Goodwin model that couples wage--employment dynamics with Minsky-style private debt. At zero real interest the interior equilibrium is nonhyperbolic and organized by a two-dimensional center manifold…

We propose a class of discrete-time stochastic models for the pricing of inflation-linked assets. The paper begins with an axiomatic scheme for asset pricing and interest rate theory in a discrete-time setting. The first axiom introduces a…

In the present paper, we investigate the optimal capital injection behaviour of an insurance company if the interest rate is allowed to become negative. The surplus process of the considered insurance entity is assumed to follow a Brownian…

While the original Ait-Sahalia interest rate model has been found considerable use as a model for describing time series evolution of interest rates, it may not possess adequate specifications to explain responses of interest rates to…

This paper develops a new stochastic volatility model for the temperature that is a natural extension of the Ornstein-Uhlenbeck model proposed by Benth and Benth (2007). This model allows to be more conservative regarding extreme events…

We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic volatility and unknown stock appreciation rate. The volatility parameter is driven by an external economic factor modeled as a…

Behavioral Foundation Models (BFMs) proved successful in producing policies for arbitrary tasks in a zero-shot manner, requiring no test-time training or task-specific fine-tuning. Among the most promising BFMs are the ones that estimate…

Optimal dividend strategy in dual risk model is well studied in the literatures. But to the best of our knowledge, all the previous works assumes deterministic interest rate. In this paper, we study the optimal dividends strategy in dual…

For environmental problems such as global warming future costs must be balanced against present costs. This is traditionally done using an exponential function with a constant discount rate, which reduces the present value of future costs.…

In econometrics, the Efficient Market Hypothesis posits that asset prices reflect all available information in the market. Several empirical investigations show that market efficiency drops when it undergoes extreme events. Many models for…

We define an infinite stochastic state machine, the Battery-Discharge-Model (BDM), which simulates the behaviour of linear and jump complexity of the continued fraction expansion of multidimensional formal power series, a relevant security…

I present the technique which can analyse some interest rate models: Constantinides-Ingersoll, CIR-model, geometric CIR and Geometric Brownian Motion. All these models have the unified structure of Whittaker function. The main focus of this…