What’s your post-Brexit investing strategy? Should you follow the markets in their flight to safety and transfer your cash to companies that should be relatively immune to the fallout? Or should you look among the shares that have slumped and search for bargains? With markets always overreacting to bad news, there are strong arguments for the latter. Here are three you might want to consider.

Top insurer?

The insurance sector has been hit along with the banks, as people have fled en masse from anything vaguely financial. As a result, we’ve seen shares in Aviva (LSE: AV) lose 14% since 23 June, to 382p today. That price fall has left Aviva shares valued at just 8.3 times forecast earnings for 2016, with EPS expected to double. And after a more modest predicted earnings rise in 2017, the P/E multiple would drop to just 7.7.

But that’s fair for a company expected to be devastated by the UK’s withdrawal from the EU, right? Well, Aviva was one of the very first to update us on its outlook immediately after the vote, saying “Aviva has conducted extensive analysis of the possible implications of a vote to leave the EU and considers it will have no significant operational impact on the company“!

With Aviva’s turnaround progress of the past few years bearing fruit, cash flow improving, and with the firm saying it has “one of the strongest and most resilient balance sheets in the UK insurance sector,” those dividend yields of 6.1% this year and 6.9% next look very attractive to me. I’d be buying if I didn’t already have some.

Housing crunch

The share price falls for housebuilders seem a little more justified, as weaker European investment in the UK property market, especially in the commercial sector, is likely to soften overall demand and perhaps weaken profits. As a result, Persimmon (LSE: PSN) shares are down 25% since the referendum, to 1,596p, although over five years they’re still up 237% and have been paying handsome dividends.

Persimmon’s business is in domestic housebuilding, and the strong demand and chronic supply shortage isn’t going to disappear any time soon. Sure, house price growth slowed and new buyer enquiries fell in the month before the vote, but that kind of uncertainty ahead of such a momentous event isn’t at all surprising.

And Persimmon’s latest update was positive, the forward P/E has dropped as low as 8.5, and there are 7% dividend yields on the cards. Looks good to me.

Airline casualty

Budget airlines could certainly suffer if we lose our access to the EU’s open skies, and the 26% price fall for easyJet (LSE: EZJ) shares as a result is perhaps not so surprising. But after June’s passenger statistics showed yet another rise over the previous year, is the fall overdone?

Although the weakening pound will surely hit the number of passengers heading from the UK to European destinations, it should do the opposite for people flying in the other direction, and with slightly more than half its business done in Europe, easyJet should at least not suffer on that score.

The fall has sent the shares’ P/E as low as 8.8 for this year and 8.1 next, and with dividend yields of 5.3% and 5.8% penciled-in, I see the fall as overkill and I rate easyJet shares as cheap now.

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Alan Oscroft owns shares of Aviva. The Motley Fool UK has no position in any of the shares mentioned. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.