Related papers: New procedures for testing whether stock price pro…
A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the discounted asset-price process - in particular, the semimartingale property is not…
A well known result in stochastic analysis reads as follows: for an $\mathbb{R}$-valued super-martingale $X = (X_t)_{0\leq t \leq T}$ such that the terminal value $X_T$ is non-negative, we have that the entire process $X$ is non-negative.…
We propose a numerical procedure for computing the prices of European options, in which the underlying asset price is a Markovian strict local martingale. If the underlying process is a strict local martingale and the payoff is of linear…
This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes.…
We extend the fundamental theorem of asset pricing to a model where the risky stock is subject to proportional transaction costs in the form of bid-ask spreads and the bank account has different interest rates for borrowing and lending. We…
The price of a stock will rarely follow the assumed model and a curious investor or a Regulatory Authority may wish to obtain a probability model the prices support. A risk neutral probability ${\cal P}^*$ for the stock's price at time $T$…
We continue study of conformal testing in binary model situations. In this note we consider Markov alternatives to the null hypothesis of exchangeability. We propose two new classes of conformal test martingales; one class is statistically…
We propose a method to bound the expectation of the supremum of the price process in stochastic volatility models. It can be applied, for example, to the rough Bergomi model, avoiding the need to discuss finiteness of higher moments. Our…
We consider a variant of sequential testing by betting where, at each time step, the statistician is presented with multiple data sources (arms) and obtains data by choosing one of the arms. We consider the composite global null hypothesis…
Some classes of increment martingales, and the corresponding localized classes, are studied. An increment martingale is indexed by the real line and its increment processes are martingales. We focus primarily on the behavior as time goes to…
The hypothesis of randomness is fundamental in statistical machine learning and in many areas of nonparametric statistics; it says that the observations are assumed to be independent and coming from the same unknown probability…
The paper proposes a class of financial market models which are based on inhomogeneous telegraph processes and jump diffusions with alternating volatilities. It is assumed that the jumps occur when the tendencies and volatilities are…
Markov processes are used in a wide range of disciplines, including finance. The transition densities of these processes are often unknown. However, the conditional characteristic functions are more likely to be available, especially for…
We propose an alternative approach for solving a number of well-studied optimal stopping problems for L\'evy processes. Instead of the usual method of guess-and-verify based on martingale properties of the value function, we suggest a more…
We give a bare-hands approach to the martingale representation theorem for integer valued random measures, which allows for a wide class of infinite activity jump processes, as well as all processes with well-ordered jumps.
The bounded mean betting procedure serves as a crucial interface between the domains of (1) sequential, anytime-valid statistical inference, and (2) online learning and portfolio selection algorithms. While recent work in both domains has…
We propose a new test to determine whether jumps are present in asset returns or other discretely sampled processes. As the sampling interval tends to 0, our test statistic converges to 1 if there are jumps, and to another deterministic and…
Comparison results for Markov processes w.r.t. function class induced (integral) stochastic orders have a long history. The most general results so far for this problem have been obtained based on the theory of evolution systems on Banach…
We develop a theory which applies to any market dynamics that satisfy a fair market assumption on the nullity of the average profit of simple market making strategies. We show that for any such fair market, there exists a martingale fair…
We study the martingale property and moment explosions of a signature volatility model, where the volatility process of the log-price is given by a linear form of the signature of a time-extended Brownian motion. Excluding trivial cases, we…