Explain why the option price should be continuous across a dividend date though the asset price experiences

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Explain why the option price should be continuous across a dividend date though the asset price experiences a jump. Using no arbitrage principle, deduce the following jump condition: 

V(S(t), t) = V(S(t), t),

where V denotes option price, td and t+d denote the time just before and after the dividend date td.

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