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Explain Four Basic Axioms of Maximising Expected Utility

I begin learn PRM , Someone help me understand Four Basic Axioms of Maximising Expected Utility most intuitive way .Thank you very much
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example Hamilton-Jacobi-Bellman Equation - clarification of $dX_t$ derivation using $\pi_t$, $\Pi_t$

I have a market with safe rate r and risky asset S $$\frac{dS_t}{S_t}=(r+Y_t)dt+\sigma dW_t \quad \quad (1)$$ $$dY_t = - \lambda Y_t +dB_t \quad \quad (2)$$ where W, B are Brownian Motions with ...
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Validity of CAPM

I came across some literature regarding "Framing Theory" or "Prospect Theory", and the validity of CAPM. I was wondering if you could shed some light on a few questions I have in this regard: ...
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Why maximize expected growth rate?

It seems to me that the optimality of the Kelly Criterion relies on the assumption that it is in an investor's best interest to maximize his portfolio's expected growth rate. Why would he care what ...
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Does risk-neutral measure have anything to deal with risk-neutrality in utility theory?

Or simply: why do we call equivalent martingale measures as risk-neutral measures? In the utility or game theory, when we consider a person's preferences to certain outcomes, we often deal with the ...
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Critique against consumption-based asset pricing theory?

I find asset pricing theory very vague and full of assumptions, especially the consumption-based modern theory. In its essence, the theory states that asset prices depend on the covariance between ...
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Why are indifference equations in mean-variance portfolio theory convex shaped

As the title suggests why is the indifference equations in mean variance portfolio theory convex shaped? Indifference Equation: https://en.wikipedia.org/wiki/Indifference_curve A graph:
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Estimating investor's utility from the trades data

Is it possible to infer investor's utility function from the set of decisions she is making? Let's assume for simplicity that the market consists of a single traded asset whose return distribution is ...
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Desired portfolio volume

I am working on a toy model, in part of which an investor has to decide (based on some utility theory) how much money to invest in a given portfolio. For simplicity, assume that the portfolio is ...