32 citations · 53 across the 7 of their papers we have counts for
11 papers
Derivation of non-classical stochastic price dynamics equations
Carey Caginalp, Gunduz Caginalp
We analyze the relative price change of assets starting from basic supply/demand considerations subject to arbitrary motivations. The resulting stochastic differential equation has…
Price equations with symmetric supply/demand; implications for fat tails
Carey Caginalp, Gunduz Caginalp
Implementing a set of microeconomic criteria, we develop price dynamics equations using a function of demand/supply with key symmetry properties. The function of demand/supply can…
A Dynamical Systems Approach to Cryptocurrency Stability
Carey Caginalp
Recently, the notion of cryptocurrencies has come to the fore of public interest. These assets that exist only in electronic form, with no underlying value, offer the owners some p…
Cryptocurrency Equilibria Through Game Theoretic Optimization
Carey Caginalp, Gunduz Caginalp
Optimization methods are used to determine equilibria of investment in cryptocurrencies. The basic assumptions involve existence of a core group (the "wealthy") that fears the loss…
Valuation, Liquidity Price, and Stability of Cryptocurrencies
Carey Caginalp, Gunduz Caginalp
Cryptocurrencies are examined through the asset flow equations and experimental asset markets. Since tangible value of a typical cryptocurrency is non-existent, the theory suggests…
The Quotient of Normal Random Variables And Application to Asset Price Fat Tails
Carey Caginalp, Gunduz Caginalp
The quotient of random variables with normal distributions is examined and proven to have have power law decay, with density , with the coeffic…
Asset Price Volatility and Price Extrema
Carey Caginalp, Gunduz Caginalp
The relationship between price volatilty and a market extremum is examined using a fundamental economics model of supply and demand. By examining randomness through a microeconomic…
Hierarchies of N-Point Functions for Nonlinear Conservation Laws with Random Initial Data
Carey Caginalp
Nonlinear conservation laws subject to random initial conditions pose fundamental problems in the evolution and interactions of shocks and rarefactions. Using a discrete set of val…
Conservation Laws With Random and Deterministic Data
Carey Caginalp
The dynamics of nonlinear conservation laws have long posed fascinating problems. With the introduction of some nonlinearity, e.g. Burgers' equation, discontinuous behavior in the…
A Minimization Approach to Conservation Laws With Random Initial Conditions and Non-smooth, Non-strictly Convex Flux
Carey Caginalp
We obtain solutions to conservation laws under any random initial conditions that are described by Gaussian stochastic processes (in some cases discretized). We analyze the general…
Minimization Solutions to Conservation Laws with Non-smooth and Non-strictly Convex Flux
Carey Caginalp
Conservation laws are usually studied in the context of sufficient regularity conditions imposed on the flux function, usually and uniform convexity. Some results are prove…