﻿<?xml version="1.0" encoding="utf-8"?>
<InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema">
  <Version>2.2.0.7</Version>
  <hasSegments>false</hasSegments>
  <ReportName>New Accounting Pronouncements</ReportName>
  <ReportLongName>01020 - Disclosure - New Accounting Pronouncements</ReportLongName>
  <DisplayLabelColumn>true</DisplayLabelColumn>
  <ShowElementNames>false</ShowElementNames>
  <RoundingOption />
  <HasEmbeddedReports>false</HasEmbeddedReports>
  <Columns>
    <Column>
      <LabelColumn>false</LabelColumn>
      <Id>1</Id>
      <Labels>
        <Label Id="1" Label="9 Months Ended" />
        <Label Id="2" Label="Sep. 30, 2010" />
      </Labels>
      <CurrencyCode>USD</CurrencyCode>
      <FootnoteIndexer />
      <hasSegments>false</hasSegments>
      <hasScenarios>false</hasScenarios>
      <Segments />
      <Scenarios />
      <Units>
        <Unit>
          <UnitID>USD</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>EPS</UnitID>
          <UnitType>Divide</UnitType>
          <NumeratorMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </NumeratorMeasure>
          <DenominatorMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>shares</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </DenominatorMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>Shares</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>shares</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
      </Units>
      <CurrencySymbol>$</CurrencySymbol>
    </Column>
  </Columns>
  <Rows>
    <Row>
      <Id>2</Id>
      <Label>Disclosure - New Accounting Pronouncements [Abstract]</Label>
      <Level>0</Level>
      <ElementName>pre_DisclosureNewAccountingPronouncementsAbstract</ElementName>
      <ElementPrefix>pre</ElementPrefix>
      <IsBaseElement>false</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ShortDefinition>No definition available.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>true</IsAbstractGroupTitle>
      <IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow>
      <IsEquityAdjustmentRow>false</IsEquityAdjustmentRow>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsReverseSign>false</IsReverseSign>
      <PreferredLabelRole />
      <IsEPS>false</IsEPS>
      <FootnoteIndexer />
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <IsRatio>false</IsRatio>
          <DisplayZeroAsNone>false</DisplayZeroAsNone>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText />
          <NonNumericTextHeader />
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDataType>xbrli:stringItemType</ElementDataType>
      <SimpleDataType>string</SimpleDataType>
      <ElementDefenition>No definition available.</ElementDefenition>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
    <Row>
      <Id>3</Id>
      <Label>New Accounting Pronouncements</Label>
      <Level>1</Level>
      <ElementName>pre_NewAccountingPronouncementsTextBlock</ElementName>
      <ElementPrefix>pre</ElementPrefix>
      <IsBaseElement>false</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ShortDefinition>For new accounting pronouncement(s) that has(have) been issued but not yet adopted, describes (1) the new pronouncement, the...</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>false</IsAbstractGroupTitle>
      <IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow>
      <IsEquityAdjustmentRow>false</IsEquityAdjustmentRow>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsReverseSign>false</IsReverseSign>
      <PreferredLabelRole>terselabel</PreferredLabelRole>
      <IsEPS>false</IsEPS>
      <FootnoteIndexer />
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <IsRatio>false</IsRatio>
          <DisplayZeroAsNone>false</DisplayZeroAsNone>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText>&lt;p style='margin-top:13.5pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;font-weight:bold;margin-left:0px;"&gt; 3.&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;font-weight:bold;"&gt; New Accounting Pronouncements&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:4.5pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:0px;"&gt;In July 2010, the FASB issued new accounting guidance which requires companies to enhance the disclosures related to the credit quality of financing receivables and the allowances for credit losses. This guidance is effective for interim and annual periods ending on or after December 15, 2010. The Company is currently evaluating the impact of the adoption of this guidance on its disclosures&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;.&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:9pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:0px;"&gt;In October 2010, the FASB issued new accounting guidance &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;clarifying that&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; only&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; acquisition costs related directly to the successful&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; acquisition of new &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;or&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; renewal &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;insurance &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;contracts &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;may &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;be capitalized. Those &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;acquisition &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;costs &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;that may be capitalized &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;include incremental direct costs&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;, such as commissions, and a portion of salaries and benefits of certain employees who are involved in underwriting and policy issuance, that are directly related to time spent on an acquired contract.&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; This guidance is effective for interim and annual periods beginning after December 15, 2011&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;,&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; with early adoption permitted at the beginning of an entity's annual reporting period&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;. The Company is currently evalu&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;a&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;ting the impact of the adoption of this guidance on &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;its&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; consolidated shareholders' equity or net income&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;.&lt;/font&gt;&lt;/p&gt;</NonNumbericText>
          <NonNumericTextHeader>3. New Accounting PronouncementsIn July 2010, the FASB issued new accounting guidance which requires companies to enhance the disclosures related to the credit</NonNumericTextHeader>
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDataType>us-types:textBlockItemType</ElementDataType>
      <SimpleDataType>textblock</SimpleDataType>
      <ElementDefenition>For new accounting pronouncement(s) that has(have) been issued but not yet adopted, describes (1) the new pronouncement, the date that adoption is required and the date that the entity plans to adopt, if earlier; (2) the methods of adoption allowed by the pronouncement and the method expected to be utilized by the entity, if determined; (3) the impact that adoption of the pronouncement is expected to have on the financial statements of the entity, unless such impact is not known or reasonably estimable (in which case, a statement to that effect shall be made) and; (4) the potential impact of other significant matters that the entity believes might result from the adoption of the pronouncement (for example, technical violations of debt covenant agreements and planned or intended changes in business practices).</ElementDefenition>
      <ElementReferences>No authoritative reference available.</ElementReferences>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
  </Rows>
  <Footnotes />
  <NumberOfCols>1</NumberOfCols>
  <NumberOfRows>2</NumberOfRows>
  <HasScenarios>false</HasScenarios>
  <MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel>
  <SharesRoundingLevel>UnKnown</SharesRoundingLevel>
  <PerShareRoundingLevel>UnKnown</PerShareRoundingLevel>
  <HasPureData>false</HasPureData>
  <SharesShouldBeRounded>true</SharesShouldBeRounded>
</InstanceReport>
