Towards a probability-free theory of continuous martingales
Without probability theory, we define classes of supermartingales, martingales, and semimartingales in idealized financial markets with continuous price paths. This allows us to establish probability-free versions of a number of standard results in martingale theory, including the Dubins-Schwarz theorem, the Girsanov theorem, and results concerning the It\^o integral. We also establish the existence of an equity premium and a CAPM relationship in this probability-free setting.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
On SDEs with Lipschitz coefficients, driven by continuous, model-free martingales
We prove the existence and uniqueness of solutions of SDEs with Lipschitz coefficients, driven by continuous, model-free martingales. The main tool in our reasoning is Picard's iterative procedure and a model-free versio…
Concentration for matrix martingales in continuous time and microscopic activity of social networks
This paper gives new concentration inequalities for the spectral norm of a wide class of matrix martingales in continuous time. These results extend previously established Freedman and Bernstein inequalities for series o…
Detecting Stochasticity in Discrete Signals via Nonparametric Excursion Theorem
We develop a practical framework for distinguishing diffusive stochastic processes from deterministic signals using only a single discrete time series. Our approach is based on classical excursion and crossing theorems f…
The extended Ville's inequality for nonintegrable nonnegative supermartingales
Following the initial work by Robbins, we rigorously present an extended theory of nonnegative supermartingales, requiring neither integrability nor finiteness. In particular, we derive a key maximal inequality foreshado…
Theory of Cryptocurrency Interest Rates
A term structure model in which the short rate is zero is developed as a candidate for a theory of cryptocurrency interest rates. The price processes of crypto discount bonds are worked out, along with expressions for th…