Research in finance often relies on a number of key assumptions which are not easily testable. In many cases these assumptions arise from the availability of existing mathematical methodology rather than empirical evidence. In the literature on pricing and also corporate finance, for instance, it is common practice to adopt the notion of underlying semi-martingale processes to facilitate computations and results from the well-developed field of stochastic processes. Statements made in terms of such semi-martingales that evolve in continuous time and in terms of agents that can control transactions in financial markets or corporate actions continuously with time, often surprise through their analytic parsimony and elegance, in particular in connection with the Markov property. The Black-Scholes-Merton formula for European option prices is one famous example. Affine models from Duffie, Filipovic, and Schachermayer (2003) are more recent contributions to the arsenal of available such models. There is no direct empirical evidence for the underlying asset price data being in fact discrete realizations of continuous-time semi-martingales, however, with some evidence against Markovianity. It is conceivable that economic statements made on the basis of such, likely unjustified, assumptions, may at least be partly spurious. This project pursues an approach independently of model assumptions. It makes statements by relying solely on trading strategies to assess tradeable implications of properties of time series of asset prices, avoiding model misspecification. Averages of profits from trading strategies are estimators of unconditional risk premia which by definition explain the structure of risk compensation in an economy. Trading strategies, other than asset pricing models, are not subject to model misspecification or estimation errors since they are model-free, but their exposure can be benchmarked to economic reference models. This project aims at developing model-free tools to investigate (i) The compensation due to higher-order risk aversion such as loss aversion. (ii) The compensation structure for deviations from independently and identically distributed (i.i.d.) asset returns. (iii) Tradeable implications of continuous vs. discontinuous semi-martingale processes. Empirical results from implementing the corresponding trading strategies will provide robust and new evidence on dynamic properties of asset prices in financial markets. They will also serve as guidelines for the specification of asset pricing models.