Related papers: New procedures for testing whether stock price pro…
Suppose we observe an infinite series of coin flips $X_1,X_2,\ldots$, and wish to sequentially test the null that these binary random variables are exchangeable. Nonnegative supermartingales (NSMs) are a workhorse of sequential inference,…
In this paper we study the pricing and hedging of nonreplicable contingent claims, such as long-term insurance contracts like variable annuities. Our approach is based on the benchmark-neutral pricing framework of Platen (2024), which…
Consider the multiple testing problem of testing k null hypotheses, where the unknown family of distributions is assumed to satisfy a certain monotonicity assumption. Attention is restricted to procedures that control the familywise error…
This work proposes a new exchangeability test for a random sequence through a martingale based approach. Its main contributions include: 1) an additive martingale which is more amenable for designing exchangeability tests by exploiting the…
In this paper we employ deep learning techniques to detect financial asset bubbles by using observed call option prices. The proposed algorithm is widely applicable and model-independent. We test the accuracy of our methodology in numerical…
A continuous-path semimartingale market model with wealth processes discounted by a riskless asset is considered. The numeraire portfolio is the unique strictly positive wealth process that, when used as a benchmark to denominate all other…
The paper is about detecting changes in the parameters of certain parameterized stochastic models. We apply CUSUM (Cumulated Sums) type test statistics that are based on martingale difference sequences.
We consider fundamental questions of arbitrage pricing arising when the uncertainty model is given by a set of possible mutually singular probability measures. With a single probability model, essential equivalence between the absence of…
A new branch based on Markov processes is developing in the recent literature of financial time series modeling. In this paper, an Indexed Markov Chain has been used to model high frequency price returns of quoted firms. The peculiarity of…
A standing assumption in the literature on proportional transaction costs is efficient friction. Together with robust no free lunch with vanishing risk, it rules out strategies of infinite variation, as they usually appear in frictionless…
Time series forecasting is widely used in a multitude of domains. In this paper, we present four models to predict the stock price using the SPX index as input time series data. The martingale and ordinary linear models require the…
A new method is proposed to obtain the risk neutral probability of share prices without stochastic calculus and price modeling, via an embedding of the price return modeling problem in Le Cam's statistical experiments framework.…
We consider the estimation of binary election outcomes as martingales and propose an arbitrage pricing when one continuously updates estimates. We argue that the estimator needs to be priced as a binary option as the arbitrage valuation…
Planning problems where effects of actions are non-deterministic can be modeled as Markov decision processes. Planning problems are usually goal-directed. This paper proposes several techniques for exploiting the goal-directedness to…
We show that the existence of an equivalent local martingale measure for asset prices does not prevent negative prices for European calls written on positive stock prices. In particular, we illustrate that many standard no-arbitrage…
In this article we show that the payment flow of a linear tax on trading gains from a security with a semimartingale price process can be constructed for all c\`agl\`ad and adapted trading strategies. It is characterized as the unique…
In this paper we introduce a new approach to model-free path-dependent option pricing. We first introduce a general duality result for linear optimisation problems over signed measures introduced in [3] and show how the the problem of…
A methodology is developed to identify, as units of study, each decrease in the value of a stock from a given maximum price level. A critical level in the amount of price declines is found to separate a segment operating under a random walk…
A new model for the stock market price analysis is proposed. It is suggested to look at price as an everywhere discontinuous function of time of bounded variation.
We obtain option pricing formulas for stock price models in which the drift and volatility terms are functionals of a continuous history of the stock prices. That is, the stock dynamics follows a nonlinear stochastic functional differential…