Asset pricing under uncertainty uses the theory of stochastic processes. Asset pricing under certainty is fairly simple: the price of an asset is the present value of its certain future payoffs discounted by a risk-free return. However, with uncertainty, stocks' and sukuks' payoffs are uncertain; pricing of these assets is no longer as simple as under certainty. Moreover, with uncertainty, many assets that do not exist in a certainty environment appear; they are called *derivatives* and have also to be priced. Theories of asset pricing under uncertainty cover stocks, sukuks, and derivatives.

Uncertainty is described in terms of a statistical probability distribution with expected mean and standard deviation. Covariance plays a role in measuring risk among assets. It is used to determine the systemic risk of an asset in relation to market portfolio. Uncertainty is also described using two random processes that dominate debate in capital market efficiency theory; these are the random walk and the martingale processes.

Even though market participants have subjective probabilities regarding the future payoff of a specific asset and may be risk averse or risk lover, they still have to agree on one common set of probabilities called *risk-neutral probabilities* to establish equilibrium price. The probability distribution of a financial asset cannot be applied to pricing the asset or derivatives on the asset without transforming it into a risk-neutral ...

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