Given the Fundamental PDE, explain the theta-gamma relation.

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The intuition for the Theta-Gamma relation is that a positive-value port- folio with a high Theta is expected to make money because of the passage of time. If it was to make more money than the risk free rate, it would be pure arbitrage, because a trader could borrow at the risk free rate, set up the portfolio, and wait. The negative convexity rebalances the pure arbitrage: the volatility in interest rates tends in average to depress the portfolio value.

Given the Fundamental PDE, Explain the Theta-Gamma Relation