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🎯 '''Expected value''' is a foundational statistical concept in the insurance industry, representing the probability-weighted average of all possible outcomes of a random variable — in insurance terms, the mean of the distribution of potential [[Definition:Losses|losses]], [[Definition:Claims|claims]], or financial results associated with a risk or portfolio. It provides the starting point for virtually every [[Definition:Actuarial science|actuarial]] calculation, from setting [[Definition:Premium|premiums]] and establishing [[Definition:Reserves|reserves]] to evaluating [[Definition:Reinsurance|reinsurance]] structures and pricing [[Definition:Insurance-linked securities|insurance-linked securities]]. While the concept is universal in probability theory, its insurance application carries particular nuance: insurers must not only estimate the expected value of losses but also layer on [[Definition:Risk margin|risk margins]], [[Definition:Expense loading|expense loadings]], and adjustments for [[Definition:Parameter uncertainty|parameter uncertainty]] to arrive at commercially viable and regulatorily compliant figures.

📐 In practice, actuaries derive expected values by summing the products of each possible loss outcome and its associated probability, or more commonly, by fitting parametric distributions to historical [[Definition:Loss experience|loss data]] and computing the mean analytically. For a [[Definition:Motor insurance|motor insurance]] portfolio, for example, the expected value of aggregate claims might be built up from frequency and severity distributions calibrated to millions of policy-years of data. In [[Definition:Catastrophe modeling|catastrophe modeling]], the expected value — often called the [[Definition:Average annual loss|average annual loss]] — emerges from tens of thousands of simulated scenarios representing different hurricane tracks, earthquake ruptures, or flood events. Under [[Definition:IFRS 17|IFRS 17]], insurers are required to produce [[Definition:Fulfilment cash flows|fulfilment cash flows]] that represent the probability-weighted mean of all future cash flow scenarios, making the expected value concept a direct regulatory requirement rather than merely a pricing convenience.

⚠️ Relying solely on expected value, however, can be dangerously misleading in insurance. Two portfolios with identical expected values may have radically different risk profiles — one might have low volatility and predictable outcomes, while the other could feature fat-tailed distributions with potential for catastrophic loss. This is why insurers supplement expected value with measures of dispersion and tail risk, such as [[Definition:Standard deviation|standard deviation]], [[Definition:Value at risk|value at risk]], and [[Definition:Tail value at risk|tail value at risk]]. Regulatory capital frameworks — including [[Definition:Solvency II|Solvency II]], the [[Definition:Risk-based capital|RBC]] system in the United States, and [[Definition:C-ROSS|C-ROSS]] in China — are explicitly designed to require insurers to hold capital well in excess of expected losses, precisely because the expected value alone fails to capture the uncertainty that defines the insurance business.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Actuarial science]]
* [[Definition:Average annual loss]]
* [[Definition:Probability distribution]]
* [[Definition:Tail value at risk]]
* [[Definition:Risk margin]]
* [[Definition:Fulfilment cash flows]]
{{Div col end}}

Definition:Expected value - Revision history

PlumBot: Bot: Creating definition