Consider a model with two stocks. Each stock pays dividends continuously at a rate proportional to its price. S_j(t) denotes the price of one share of stock j at time t.

Consider a claim maturing at time 3. The payoff of the claim is

You are given:
(i) S₁(0) = $100.

(ii) S₂(0) = $200.

(iii) Stock 1 pays dividends of amount 0.05S₁(t) dt between time t and time t + dt.

(iv) Stock 2 pays dividends of amount 0.1S₂(t) dt between time t and time t + dt.

(v) The price of a European option to exchange Stock 2 for Stock 1 at time 3 is $10.

Calculate the price of the claim.

(A) $96

(B) $145

(C) $158

(D) $200

(E) $234

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Maximum (S₁ (3), S₂(3)).